# Question: what kind of diff. eq is that?

• October 26th 2008, 08:15 AM
JrShohin
Question: what kind of diff. eq is that?

What kind of diff.eq. is that? I don't have any idea from where to begin with (Shake)
• October 26th 2008, 08:20 AM
ThePerfectHacker
Quote:

Originally Posted by JrShohin

What kind of diff.eq. is that? I don't have any idea from where to begin with (Shake)

The solution to the equation,
$y'' + y = 0$
Is given by $y=c_1\sin x + c_2\cos x$

Here you have the equation,
$y''+y = x$
Thus you need to find a particular solution.
By inspection it is easy to see that $y=x$ works.

Thus, the full solution is $y=c_1\sin x + c_2\cos x + x$
• October 26th 2008, 07:08 PM
Black Kawairothlite
this is a second grade ordinary differential equation and you solve it by getting the characteristic equation which in this case is:

$m^2+1=0$

then

$m=\sqrt{-1}= i$ (+ or - )

and then you gotta use the standard solutions for complex numbers and u will get:

$

y=c_1\sin x + c_2\cos x

$

but this is the general solution of the eq. so u gotta apply the parameters variation method or the undefined coefficient method to get the particular solution or also by inspection as the mod said

(Hi)