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

• Oct 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)
• Oct 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,
$\displaystyle y'' + y = 0$
Is given by $\displaystyle y=c_1\sin x + c_2\cos x$

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

Thus, the full solution is $\displaystyle y=c_1\sin x + c_2\cos x + x$
• Oct 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:

$\displaystyle m^2+1=0$

then

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

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

$\displaystyle y=c_1\sin x + c_2\cos x$

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)