Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

$\begin{array}{rl}& \frac{dy}{dx}+\frac{1}{x}\cdot y=\sin x\left[\text{ Type }\frac{dy}{dx}+Py=Q\right]\\ & e^{\int Pdx}=e^{\int \frac{1}{x}dx}=e^{\log x}=x\end{array}$ $\therefore$ Sol. is $\mathrm{yx}=\int \mathrm{x}\sin \mathrm{xdx}+\mathrm{C}$ $\begin{array}{rl}& =x(-\cos x)-\int 1\cdot (-\cos x)dx+C\\ & =-x\cos x+\sin x+C\Rightarrow x(y+\cos x)=\sin x+C\end{array}$