If f(x)=( x) and f''(x)+ x,f'(x)+g(x)=0, then g(x) is:

Question

If $f(x)=\sin(\sin x)$ and $f''(x)+	an x\,f'(x)+g(x)=0$, then $g(x)$ is:

Accepted Answer

$f'(x)=\cos(\sin x)\cos x$. $f''(x)=-\sin(\sin x)\cos^2x-\cos(\sin x)\sin x$.

$g(x)=-f''(x)-	an x\,f'(x)=\cos^2x\sin(\sin x)+\sin x\cos(\sin x)-	an x\cos x\cos(\sin x)=\cos^2x\sin(\sin x)$.

Solutions · 1