Homework Help: Assistance with Third Order Differential Equation

1. Dec 5, 2013

kelvin2013

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

Just wondering if anyone knows how to solve the following as I am not sure where to start at all:

y''' + 8y = xsin(2x)

Any help would be great.

2. Relevant equations

3. The attempt at a solution

I'm thinking solving the homogeneous DE y'''+8y = 0 and then as far as I can see a possible solution maybe of the form yp=Axsin(2x)+Bxcos(2x)+Csin(2x)+Dcos(2x) ?

2. Dec 5, 2013

LCKurtz

What do you get for $y_c$ when you solve the homogeneous DE? You need to know that before you can predict the form of the NH equation.

3. Dec 5, 2013

kelvin2013

Hi,

thanks for the reply - I get:

yp=c1e-2x+c2e(1+i√3)x+c3e(1-i√3)x

?

4. Dec 5, 2013

LCKurtz

OK. So far so good. It would be nicer to use sines and cosines instead of the complex exponentials. Anyway, your complementary solution doesn't contain any terms like the NH term. So what happens when you try your proposed $y_p$?

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