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

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- Oct 26th 2008, 08:15 AMJrShohinQuestion: what kind of diff. eq is that?
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What kind of diff.eq. is that? I don't have any idea from where to begin with (Shake) - Oct 26th 2008, 08:20 AMThePerfectHacker
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 PMBlack 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)