# Thread:

1. ## 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

2. Originally Posted by JrShohin

What kind of diff.eq. is that? I don't have any idea from where to begin with
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 $y=c_1\sin x + c_2\cos x + x$

3. 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:

$<br /> <br /> y=c_1\sin x + c_2\cos x<br /> <br />$

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
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