# Homework Help: Simple NonHomogenous Differential Equation Question

1. Nov 24, 2009

### shards5

1. The problem statement, all variables and given/known data
y"' -9y" +18y" = 30ex. Does not matter what the initial conditions are for my question.

2. Relevant equations
N/A

3. The attempt at a solution
So I factored out the equation and got:
r*(r2 - 9r + 18)
Which gives roots r = 0, r = 3, r = 6.
Which gives me the general solution:
y(x) = C0*1 + C1e3x + C2e6x
Is the above general solution correct?
Next question I have is whether I solved for the yp correctly.
yp = A*ex
yp' = A*ex
yp" = A*ex
yp'" = A*ex
which by plugging into the equation will give.
A*ex - 9A*ex + 18A*ex = 30ex
which gives 10A*ex = 30ex
which gives A = 3.
Which means my general solution should be.
y(x) = y(x) = C0*1 + C1e3x + C2e6x +3*ex
Is all this correct because I am trying to solve for the "C0, C1, etc." and I want to be absolutely sure that the base I am working with is correct and that my error is just a miscalculation with the initial conditions. Thanks.

2. Nov 24, 2009

### LCKurtz

At first glance it looks OK to me. But if you really want to be sure, all you have to do is substitute your general solution back in to the DE and see if it works.

3. Nov 24, 2009

### shards5

Hmm didn't think about substituting back into the original DE. Thanks a lot for the tip.