Laplace Transform solution for 2nd order differential equation

[khnbaba]

Homework Statement

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

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

Homework Equations

i can't figure out how to derive the values of A, B, and C from the attempted equation solution. please help me out here. thanks

The Attempt at a Solution

 

[SteamKing]

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.

 

[khnbaba]

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

 

[khnbaba]

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

 

[SteamKing]

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?

 

[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.

 

[SteamKing]

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.

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.

 

[khnbaba]

thanks a lot for your time and efforts.