y=e^rt Nonlinear Bernoulli DE Alternating Series Test Linear 2nd order DE w constant coefficents

Linear 2nd order DE w constant coefficents

use yp to find y' & y'' -plug back in Linear 2nd order DE w constant coefficents trig identities : Method of undetermined coefficients Maclaurin 1/(1-x)

Method of undetermined coefficients

y=c1x+c2/x u1'x +u2'/x =0 u1'y1' + u2'y2' = F(x)/P(x) U1' = delta 1/delta Method of Variation of Parameters Maclaurin 1/(1-x) Reduction of order E^x

Method of Variation of Parameters

Graph of Exponential Parent Function Graph of Reciprocal Equation for Cubic Graph of Linear Parent Function

Graph of Linear Parent Function

Equation for Quadratic Graph of Absolute Value Parent Function Equation of Reciprocal Graph of Linear Parent Function

Graph of Absolute Value Parent Function

Equation for Absolute Value Graph of Exponential Parent Function Equation for Square Root Graph of Quadratic Parent Function

Graph of Quadratic Parent Function

Graph of Reciprocal Equation for Exponential Graph of Square Root Parent Function Graph of Exponential Parent Function

Graph of Square Root Parent Function

Equation for Cubic Equation of Reciprocal Graph of Exponential Parent Function Equation for Absolute Value

Graph of Exponential Parent Function

V(0-) = V(0+) = V(0) Rule for continuousness in Capacitors and inductors Solution for capacitors is written in terms of... Solution for inductors is written in terms of.... Tao time constant for capacitors

Rule for continuousness in Capacitors and inductors

y(t) = (yo - b/a)e^-(at) + b/a I(t) for capacitors Vc(t=oo) is equal to... Tao time constant for inductors Solution to ODE with the form of dy/dt + ay = b

Solution to ODE with the form of dy/dt + ay = b

zero-state) b/a(1-e^-at) - zero state brings the initial condition (yo) to be zero Zero-state in solution y(t) = (yo - b/a)e^-(at) + b/a Steps for solving y(t) = Ae^(-at) + B I(t) for capacitors Vc(t=oo) is equal to...

Zero-state in solution y(t) = (yo - b/a)e^-(at) + b/a

zero-input) yoe^-at - zero input brings the b/a(1-e^-at) to zero Zero-input in solution y(t) = (yo - b/a)e^-(at) + b/a Tao time constant for inductors Tao time constant for capacitors Zero-state in solution y(t) = (yo - b/a)e^-(at) + b/a

Zero-input in solution y(t) = (yo - b/a)e^-(at) + b/a

Tao = L/Rt Tao time constant for inductors Tao time constant for capacitors Solution for inductors is written in terms of.... Vc(t=oo) is equal to...

Tao time constant for inductors

Tao = RtC Solution for capacitors is written in terms of... Tao time constant for capacitors Rule for continuousness in Capacitors and inductors V(t) for inductors

Tao time constant for capacitors

Rearrange so that N(y)dy = M(x)dx - Integrate both sides and solve Solve the equation of the form y' = f(x) How can one solve for a second solution of the equation a0(t)y''+a1(t)y'+a2(t)y=0 given its Wronskian W and one of its solutions y₁ How to solve an exact equation M(x)dx + N(y)dy = 0 Solve the equation of the form dy/dx = M(x)/N(y)

Solve the equation of the form dy/dx = M(x)/N(y)

Rearrange so that (1/y)dy = -p(t)dt - Integrate on both sides and solve Solve the equation of the form y' + p(t)y = 0 When solving the equation of the form a0(t)y''+a1(t)y'+a2(t)y=g(t) by Method of Undetermined Coefficients, what particular solution should you guess with if g(t) is a trigonometric function What is the Wronskian of 2 solutions y₁ and y₂ What is cosh(t)

Solve the equation of the form y' + p(t)y = 0

Find u(t) such that u'(t) = u(t)p(t) - Multiply both sides of the equation by u(t) - Simplify and integrate What is the solution of ax²y''+bxy'+cy=0 given that its roots k₁=k₂ What relationship between the equation a0(t)y''+a1(t)y'+a2(t)y=0 and its Wronskian is useful for confirming the validity of its answer What is the solution of ay''+by'+cy=0 given that its roots k₁,₂=a±Bi Solve the equation of the form y' + p(t)y = g(t) using method of integrating factors

Solve the equation of the form y' + p(t)y = g(t) using method of integrating factors

Find the solution of y' + p(t)y = 0 - Replace the unknown constant C with the unknown equation u - Sub homogenous solution into inhomogenous equation and solve for u - Plug u value into homogenous solution to find the inhomogenous solution How do you know if an integrating factor for M(x)dx + N(y)dy = 0 is a function u(y)? What is u(y)? Solve the equation of the form y' + p(t)y = g(t) using method of variation of parameters Solve the equation of the form y' = f(y/x) How do you know if an integrating factor is a function u(xy)? What is u(xy)?

Solve the equation of the form y' + p(t)y = g(t) using method of variation of parameters

Divide both sides by yⁿ - Sub into the equation z = y¹⁻ⁿ and z' = y'*(y¹⁻ⁿ)' - Solve as you would an inhomogenous equation - Sub y¹⁻ⁿ back into general solution Solve the equation of the form y' + p(t)y = g(t)yⁿ Solve the equation of the form dy/dx = M(x)/N(y) What is the solution of ay''+by'+cy=0 given that its roots k₁,₂=a±Bi How to solve an exact equation M(x)dx + N(y)dy = 0

Solve the equation of the form y' + p(t)y = g(t)yⁿ

Sub ux into y to get (ux)' = f(u) - Solve new equation as a seperable equation for x - To find the solution for y, multiply x's solution by u What is the solution of ax²y''+bxy'+cy=0 given that its roots k₁≠k₂ When solving the equation of the form a0(t)y''+a1(t)y'+a2(t)y=g(t) by Method of Undetermined Coefficients, what particular solution should you guess with if g(t) is a trigonometric function Solve the equation of the form y' + p(t)y = g(t) using method of variation of parameters Solve the equation of the form y' = f(y/x)

Solve the equation of the form y' = f(y/x)

Rearrange so that dy = f(x)dx - Integrate both sides and solve What form must you convert a 2nd Order Euler's Equation ax²y''+bxy'+cy=0 into in order to solve Solve the equation of the form y' + p(t)y = 0 When solving the equation of the form a0(t)y''+a1(t)y'+a2(t)y=g(t) by Method of Undetermined Coefficients, what particular solution should you guess with if g(t) is a polynomial Solve the equation of the form y' = f(x)

Solve the equation of the form y' = f(x)

An equation M(x,y)dx + N(x,y)dy = 0 is exact if and only if Mdy = Ndx How to tell if the equation M(x,y)dx + N(x,y)dy = 0 is Exact How to solve an exact equation M(x)dx + N(y)dy = 0 What form is the general solution of a0(t)y''+a1(t)y'+a2(t)y=0 How do you know if an integrating factor is a function u(x)? What is u(x)?

How to tell if the equation M(x,y)dx + N(x,y)dy = 0 is Exact

Integrate M(x,y) by x and N(x,y) by y, but replace the unknown constance C1 and C2 with the unknown equations f and g - Find the values f and g such that both integrals equal eachother - The similar equation + C is the solution What form must you convert a 2nd Order Euler's Equation ax²y''+bxy'+cy=0 into in order to solve How can one solve for a second solution of the equation a0(t)y''+a1(t)y'+a2(t)y=0 given its Wronskian W and one of its solutions y₁ How to solve an exact equation M(x)dx + N(y)dy = 0 Solve the equation of the form dy/dx = M(x)/N(y)

How to solve an exact equation M(x)dx + N(y)dy = 0

If [Ndx - Mdy]/M is a function g(y), then the integrating factor is the function u(y) such that ln(u(y)) = ∫g(y)dy Solve the equation of the form y' = f(x) When solving the equation of the form a0(t)y''+a1(t)y'+a2(t)y=g(t) by Method of Undetermined Coefficients, what particular solution should you guess with if g(t) is of the form Ceᵈᵗ for some constants C,d, and eᵈᵗ can be found in the homogenous equation's solution Solve the equation of the form a0(t)y''+a1(t)y'+a2(t)y=g(t) using the method of variation of parameters How do you know if an integrating factor for M(x)dx + N(y)dy = 0 is a function u(y)? What is u(y)?

How do you know if an integrating factor for M(x)dx + N(y)dy = 0 is a function u(y)? What is u(y)?

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