0
$\begingroup$

Find general solution of the ODE:

$\dfrac{\operatorname{d^2y}}{\operatorname{dx^2}}+y=f(x)$ where $f(x) $ is a real valued continuous function on $(-\infty,\infty)$

C.F: $D\equiv \dfrac{\operatorname{d^2}}{\operatorname{dx^2}}$ then $D^2+1=0$.

Hence $y=A\cos x+ B\sin x$.

I can't find the particular integral .

$\endgroup$
  • 2
    $\begingroup$ use the variation of parameters $\endgroup$ – E.H.E Dec 1 '15 at 16:38
0
$\begingroup$

It looks as if this has been asked before:

Finding the general solution of the differential equation $\,\,y''+y=f(x)$

According to this post, you are missing a $\ldots+\int_{0}^{x} \sin(x-t)f(t) \ dt$ at the end.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for?Browse other questions tagged or ask your own question.