Differential equations - undetermined coefficients

• Mar 11th 2009, 09:55 PM
ubique
Differential equations - undetermined coefficients
Hey guys!
I have a quiz tomorrow and i'm not going to be able to sleep unless I understand the solution to this question. it's long, I kinda feel bad even asking (Doh)

Anyway the question is:

Use method of undetermined coefficients to find the particular solution to

y''' - 3y'' + 4y = e^2x

I took my yp = x^2 * Ae^2x
I multipllied by x^2 because of the double roots ( I got 2,2,-1 for roots)

Thanks so much to anyone who can help me... I know its a long one.
• Mar 12th 2009, 09:21 AM
Coomast
Quote:

Originally Posted by ubique
Hey guys!
I have a quiz tomorrow and i'm not going to be able to sleep unless I understand the solution to this question. it's long, I kinda feel bad even asking (Doh)

Anyway the question is:

Use method of undetermined coefficients to find the particular solution to

y''' - 3y'' + 4y = e^2x

I took my yp = x^2 * Ae^2x
I multipllied by x^2 because of the double roots ( I got 2,2,-1 for roots)

Thanks so much to anyone who can help me... I know its a long one.

Hello ubique,

You are doing the right thing. Just take the derivatives of this and substitute it in the DE. You will see that it gives you the value of A directly.

p.e. the first derivative is:

$y'_p=2A(x+x^2)e^{2x}$

Let us know if this helps,

Coomast