Question: In Problems y = c 1 e 3x + c 2 e x 2x is a two parameter family of the second-order DE y''

In Problems y = c₁e^3x + c₂e^x 2x is a two parameter family of the second-order DE y'' 2y' 3y = 6x + 4. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.

1. y (0) = 0, y'(0) = 0

2. y (0) = 1, y'(0) = 3

3. y (1) = 4, y'(1) = -2

4. y (1) = 0, y'(1) = 1

Step by Step Solution

★★★★★

3.46 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

1 If y0 0 and y0 0 then c 1 c 2 0 3c 1 c 2 2 0 So c 1 12 and c 2 12 Thus y 12 e 3x half e x ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (2 attachments)

1596_6062c74cf3293_674971.pdf

180 KBs PDF File

1596_6062c74cf3293_674971.docx

120 KBs Word File

Students Have Also Explored These Related First Course Differential Equations Questions!

In Problems 1-3, sketch the solid S. Then write an iterated integral for 1. S = {(x, y, z): 0 ( x ( 1, 0 ( y ( 3, 0 ( z ( 1/6(12 - 3x - 2y)} 2. S = {(x, y, z): 0 ( x ( (4 - y2, 0 ( y ( 2, 0 ( z ( 3}...

In Problems 1-3, use Green's Theorem to evaluate the given line integral. Begin by sketching the region S? 1. Where C is the closed curve formed by y = x / 2 and y = (x between (0, 0) and (4, 2)? 2....

In Problems 1-3, evaluate? 1. g(x, y, z) = x2 + y2 + z; G: z = x + y + 1, 0 ( x ( 1, 0 ( y ( 1 2. g(x, y, z) = x; G: x + y + 2z = 4, 0 ( x ( 1, 0 ( y ( 1 3. g(x, y, z) = x + y; G: z = (4 - x2, 0 ( x...

0.0/ 2.5 Points 1. Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 31-x = 1/27 A. {2} B. {-7} C. {4} D. {3} 2.5 Points 2....

Table of contents / Unit 6 ~ Equations and Inequalities / Quiz 6 - Equations and Inequalities Quiz navigation Time left 1: 03:12 1 2 3 5 6 8 9 10 11 12 13 14 15 16 Question 3 Match each system of...

answer the following questions - 1 1 0 1 Consider the matrices F = 0 O , and H = 0 3 .Which of these matrices is/are invertible? -2 2 -2 3 0 4 O A. G only O B. F only O C. H only O D. All of them O...

$3. 3(y - 2)2 - 7 $4. (1 -t)2 - (1 - t) 1 - 2 In Exercises $5-$11, solve the equation for y. $9. x = Vy-2 88. * = 4y 1 -y $5. x = 3y -4 $6. 4x - 3y=7 $11. x = 5 -(2y) Sil ty -4 EXERCISES In Exercises...

EXAMPLE 9 Since f(x) = (tan x)/ (1 + x2 + x4) satisfies f(-x) = -f(x), it is odd and so tan x -1+12 + , 4 dx =0 4.5 EXERCISES 1-6 Evaluate the integral by making the given substitution. dt 23. /1+ 23...

Practice Exercises Part A. Directions: Answer these questions without using your calculator. In Questions 1-10, a(t) denotes the acceleration function, v(t) the velocity function, and s(t) the...

NAME SUBJECT DATE 2 TF 10 11 12 13 14 15 IABCDE 2ABCDE 3ABCDE 4ABCDE SABCDE BABCDE 17 18 19 20 7ABCDE ABCDE ABCDE 21 3 10 ABCDE MAB HABCDE SABC 12 ABCDE MABC 24 2 -5 13ABCDE 14 ABCDE SABCO 26 MABCDE...

The wire segment in Figure carries a current of 1.8 A from a to b. There is a magnetic field B = 1.2 T k. Find the total force on the wire and show that it is the same as if the wire were a straight...

give a clear exploration of the differences between astral and anastral mitosis?

Lily did not order two (of) these cars, (nor) has she ordered any other vehicles (through) our dealership (during) September

3.5 Compute the weighting class estimate (3.6) of the mean cholesterol level in the population and its estimated mean squared error (3.7). Thereby construct an approximate 95% confidence interval for...

Match the given graph with one of the functions in (a)(f ). The graph of f (t) is given in Figure 7.3.10. (a) f(t) f(t) U(t a) (b) f(t b) Ut b) (c) f(t) U(t a) (d) f(t) f() U(t b) (e) f(t) U(t...

In problem use Theorem 7.4.3 to find the Laplace transform of the given periodic function. THEOREM 7.4.3 If f (t) is piecewise continuous on [0, ), of exponential order, and periodic with period T,...

If {f(t)} = F(s) and a > 0 is a constant, show that This result is known as the change of scale theorem. L{ffat)} a a

Write a brief summary to clearly layout how much money the investor should invest in each stock in the optimal risk portfolio and what is the risk of the portfolio. Compare to individual stocks, what...

Write a C program, to solve the quadratic equation a x 2 + b x + c = 0 of given coefficients a, b and c. When running the program, it prompts for the input of coefficients a,b,c as floating numbers....

Question As part ofa survey, 16 adults were asked. "How many hours did you spend at yourjob last week?" The results are shown in the stemandleaf display below. Use the display to answer the questions...