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mathematics
first course differential equations

Questions and Answers of First Course Differential Equations

A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the improved Euler method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the Runge–Kutta method with step sizes h = 0.2, 0.1, 0.05, and 0.025 to approximate to six
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the improved Euler method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use Euler’s method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to four decimal
In each of Problems 23-30, a second-order differential equation and its general solution y(x) are given. Determine the constants A and B so as to find a solution of the differential equation that
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.4x1 - 2x2 - 3x3 + x4 =
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.x1 + x2
Find the reduced echelon form of each of the matrices given in Problems 1–20. 3 6 5 10 4 352 1 7 8 18 5 9 13 47 26
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.2x1 + 4x2 - x3 - 2x4 + 2x5 = 6x1 + 3x2 +
Find the reduced echelon form of each of the matrices given in Problems 1–20. 2 1 3 -4 0 2 L 1 7-10-19 13 6 13 -8
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.3x1 + x2 + x3 + 6x4 = 14x1 - 2x2 + 5x3 -
Find the reduced echelon form of each of the matrices given in Problems 1–20. 1 11 1 -2 -2 3-1 -1 -4 8-1 11 3
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 + x2 + 2x3 = 5 x2 + 3x3 = 6
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the improved Euler method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the Runge–Kutta method with step sizes h = 0.2, 0.1, 0.05, and 0.025 to approximate to six
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the improved Euler method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use Euler’s method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to four decimal
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the Runge–Kutta method with step sizes h = 0.2, 0.1, 0.05, and 0.025 to approximate to six
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use Euler’s method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to four decimal
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the Runge–Kutta method with step sizes h = 0.2, 0.1, 0.05, and 0.025 to approximate to six
Find the reduced echelon form of each of the matrices given in Problems 1–20. 3 نیا
Find the reduced echelon form of each of the matrices given in Problems 1–20. 3] 3 7 25
Find the reduced echelon form of each of the matrices given in Problems 1–20. 3 7 5 2 15 11
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.2x1 - 5x2 + x3 = 2 3x2 - 2x3 = 9
Find the reduced echelon form of each of the matrices given in Problems 1–20. 3 7 5 2 -1 8
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 - 3x2 + 4x3 = 7 x2 - 5x3 = 2
Find the reduced echelon form of each of the matrices given in Problems 1–20. 2 -11 2 3 -19
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 - 5x2 + 2x3 = 10 x2 - 7x3 = 5
Find the reduced echelon form of each of the matrices given in Problems 1–20. จาก 4 -7
Find the reduced echelon form of each of the matrices given in Problems 1–20. L 12 2 1 3 1 4 219
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 + x2 - 2x3 + x4 = 9 X2 - X3 + 2x4 = 1
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 - 2x2 + 5x3 - 3x4 = 7 x2 - 3x3 + 2x4 = 3
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 + 2x2 + 4x3 - 5x4 = 17 x2 - 2x3 + 7x4 = 7
Find the reduced echelon form of each of the matrices given in Problems 1–20. 1 -4 3 -9 1-2 -5 3 3 نیا نیا
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 - 10x2 + 3x3 - 13x4 = 5 x3 +
Find the reduced echelon form of each of the matrices given in Problems 1–20. 5 2 01 L 4 1 18 4 12
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.2x1 + x2 + x3 + x4 = 6 3x2 - X3 - 2x4 = 2
Find the reduced echelon form of each of the matrices given in Problems 1–20. -7 577 24 1 594
The linear systems in Problems 1–10 are in echelon form. Solve each by back substitution.x1 - 5x2 + 2x3 - 7x4 + 11x5 = 0 x2 - 13x3 + 3x4 - 7x5 = 0
Find the reduced echelon form of each of the matrices given in Problems 1–20. 32 1 9 1 6 7 3-6
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.2x1 + 8x2 + 3x3 = 2x1 + 3x2 + 2x3 = 52x1
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.3x1 + x2 - 3x3 = 62x1 + 7x2 + x3 = -92x1
Find the reduced echelon form of each of the matrices given in Problems 1–20. 1 32 12 -4-2 1 5 -12 -8
Find the reduced echelon form of each of the matrices given in Problems 1–20. c 1 26 Ժ Ա + Ո 4
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.x1 + 3x2 + 3x3 = 132x1 + 5x2 + 4x3 =
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.3x1 - 6x2 - 2x3 = 12x1 - 4x2 + x3 = 17x1
Find the reduced echelon form of each of the matrices given in Problems 1–20. 122 357 227 53 7 7 22
Find the reduced echelon form of each of the matrices given in Problems 1–20. 2 2 1 -1 2 7 4 -4 19 2 23 -3
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.2x1 + 5x2 + 12x3 = 63x1 + x2 + 5x3 =
Find the reduced echelon form of each of the matrices given in Problems 1–20. 1 3 15 2 4 22 2 7 34 7 7x 8 17
In Problems 11–22, use elementary row operations to transform each augmented coefficient matrix to echelon form. Then solve the system by back substitution.x1 - 4x2 - 3x3 - 3x4 = 42x1 - 6x2 -5x3 -
In each of Problems 1–22, use the method of elimination to determine whether the given linear system is consistent or inconsistent. For each consistent system, find the solution if it is unique;
Find the reduced echelon form of each of the matrices given in Problems 1–20. 1 2 L 2 -2 -5 3 18 5 5 26 -12 11 21 1 9 11
This problem outlines a proof that two linear systems LS1 and LS2 are equivalent (that is, have the same solution set) if their augmented coefficient matrices A1 and A2 are row equivalent.(a) If
Show that the two matrices in (1) are both row equivalent to the 3 x 3 identity matrix (and hence, by Theorem 1, to each other). THEOREM 1 Unique Reduced Echelon Form Every matrix is row equivalent
A system of the forma1x + b1y = 0a2x + b2y = 0,in which the constants on the right-hand side are all zero, is said to be homogeneous. Explain by geometric reasoning why such a system has either a
Show that the 2 x 2 matrixis row equivalent to the 2 x 2 identity matrix provided that ad - bc ≠ 0. A = [a b d
The linear systema1x + b1y = c1a2x + b2y = c2a3x + b3y = c3of three equations in two unknowns represents three lines L1, L2, and L3 in the xy-plane. Figure 3.1.5 shows six possible configurations of
List all possible reduced row-echelon forms of a 3 x 3 matrix, using asterisks to indicate elements that may be either zero or nonzero.
Consider the homogeneous system(a) If x = x0 and y = y0 is a solution and k is a real number, then show that x = kx0 and y = ky0 is also a solution.(b) If x = x1, y = y1 and x = x2, y = y2 are both
Consider the linear systema1x + b1y + c1z = d1a2x + b2y + c2z = d2a3x + b3y + c3z = d3of three equations in three unknowns to represent three planes P1, P2, and P3 in xyz-space. Describe the solution
Let E be an echelon matrix that is row equivalent to the matrix A. Show that E has the same number of nonzero rows as does the reduced echelon form E* of A. Thus the number of nonzero rows in an
Apply Euler’s method with successively smaller step sizes on the interval [0,2] to verify empirically that the solution of the initial value problemhas a vertical asymptote near x = 2.003147.
The general solution of the equationis y(x) = tan(C + sin x) With the initial condition y(0) = 0 the solution y(x) = tan(sin x) is well behaved. But with y(0) = 1 the solution y(x) = tan (1/4π sin
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use Euler’s method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to four decimal
Use the improved Euler method with a computer system to find the desired solution values in Problems 27 and 28. Start with step size h = 0.1, and then use successively smaller step sizes until
Use Euler’s method with a computer system to find the desired solution values in Problems 27 and 28. Start with step size h = 0.1, and then use successively smaller step sizes until successive
A computer with a printer is required for Problems 17 through 24. In these initial value problems, use the improved Euler method with step sizes h = 0.1, 0.02, 0.004, and 0.0008 to approximate to
Use the improved Euler method with a computer system to find the desired solution values in Problems 27 and 28. Start with step size h = 0.1, and then use successively smaller step sizes until
Use the Runge–Kutta method with a computer system to find the desired solution values in Problems 27 and 28. Start with step size h = 1, and then use successively smaller step sizes until
Consider the initial value problem(a) Solve this problem for the exact solutionwhich has an infinite discontinuity at x = 0.(b) Apply Euler’s method with step size h = 0.15 to approximate this
Use the Runge–Kutta method with a computer system to find the desired solution values in Problems 27 and 28. Start with step size h = 1, and then use successively smaller step sizes until
Use Euler’s method with a computer system to find the desired solution values in Problems 27 and 28. Start with step size h = 0.1, and then use successively smaller step sizes until successive
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.x3 + 3y - xy' = 0
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.(x + y) y' = x - y
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.xy2 + 3y2 - x2y' = 0
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.2xy y' = x2 + 2y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.xy + y2 - x2y' = 0
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.xy' = y + 2√xy
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.2xy3 + ex + (3x2y2 + sin y) y' = 0
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.(x - y) y' = x + y
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.3y + x4y' = 2xy
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.x(x + y) y' = y(x - y)
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.2xy2 + x2y' = y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.(x + 2y) y' = y
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.2x2y + x3y' = 1
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.xy2y' = x3 + y3
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.xy' + 2y = 6x2 √y
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout. xy' = y + √√x² + y²
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.2xy + x2y' = y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.x2y' = xy + x2 ey/x
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout. xyy = y2 + xv4x2+y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout. yy' + x = √√√√x² + y² x2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.x2y' = xy + y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.y' = 1 + x2 + y2 + x2y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.xyy' = x2 + 3y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout. y' = = √√√x+y+I
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.x2y' = xy + 3y2
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x throughout.(x2 - y2)y' = 2xy
Find general solutions of the differential equations in Problems 1 through 30. Primes denote derivatives with respect to x.6xy3 + 2y4 + (9x2y2 + 8xy3)y' = 0

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