# Homework Help: Laplace Transform solution for 2nd order differential equation

1. May 11, 2014

### khnbaba

1. The problem statement, all variables and given/known data

d^2x/dt^2 - 3 dx/dt + 2x= 2e^3t

give that at t=0, x=5, and dx/dt=7

2. Relevant equations
i cant figure out how to derive the values of A, B, and C from the attempted equation solution. please help me out here. thanks

3. The attempt at a solution

2. May 11, 2014

### SteamKing

Staff Emeritus
You've got three simultaneous equations in three unknowns, A, B, and C.

You can use elimination, Cramer's rule, guessing, whatever to solve for A, B, and C.

You've done good work up to this point. I'm surprised this point has stumped you.

3. May 11, 2014

### khnbaba

thanks alot steamKing you are being a big help, i went through cramer's rule examples and i think its gonna solve my problem, i am gonna try it now. plus i will learn some thing new :). i really appreciate your help. once again thanks

4. May 11, 2014

### khnbaba

SteamKing can you have a look to the final answer. thanks

5. May 11, 2014

### SteamKing

Staff Emeritus
For the second and third equations in your original system, for some reason you have the coefficients of A and C switched around.

Check your arithmetic in calculating the coefficients from the steps above that point, specifically where you let s = 0. Is the product of two negative numbers another negative number?

6. May 11, 2014

### khnbaba

are you talking about equation 2, and eq 3 in the beginning?
and s=0 was just a supposition and the arithmetic below isn't part of the question which i realize now the product of two negative numbers should be positive not negative.

7. May 11, 2014

### SteamKing

Staff Emeritus
Yes. It appeared from your work that the calculations where s = 0 is where you started to calculate the coefficients of A, B, and C.

8. May 11, 2014

### khnbaba

thanks alot for your time and efforts.