# diff eqn with cos and i?

• Mar 11th 2009, 12:02 PM
fiksi
diff eqn with cos and i?
Here it is...
d2y/dx2 + 4y=cos(x) , y(0)=1, dy/dx(0)=1. If I am correct, lambda is for this one 2i and -2i. I'm not sure if i'm doing this right... in any case, what do with this cos(x)?

How to solve this? And what do u get? I'm kinda stuck...
• Mar 11th 2009, 02:55 PM
Jester
Quote:

Originally Posted by fiksi
Here it is...
d2y/dx2 + 4y=cos(x) , y(0)=1, dy/dx(0)=1. If I am correct, lambda is for this one 2i and -2i. I'm not sure if i'm doing this right... in any case, what do with this cos(x)?

How to solve this? And what do u get? I'm kinda stuck...

Yes on 2i, -2i. Your complimentary solution is

$y_c = c_1 \sin 2x + c_2 \cos 2x$. It obtain a particualr solution, try a form $y_p = A \sin x + B \cos x$, sub into the ODE and compare terms. This will give you an A and B. Then use your IC's.
• Mar 11th 2009, 03:25 PM
fiksi
if i get u correctly, trying this...

i get final solution y=1/3cosx + 1/2sin(2x)+ 2/3 cos(2x). Is that it?
• Mar 11th 2009, 04:13 PM
Jester
Quote:

Originally Posted by fiksi
if i get u correctly, trying this...

i get final solution y=1/3cosx + 1/2sin(2x)+ 2/3 cos(2x). Is that it?

Yep (Clapping)