\[ x^2 (-\sin (x))+x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.0220928 (sec), leaf count = 15
\[\{\{y(x)\to -x \cos (x)+c_1 x\}\}\] ✓ Maple : cpu = 0.007 (sec), leaf count = 12
\[y \relax (x ) = \left (-\cos \relax (x )+c_{1}\right ) x\]
Hand solution
\[ xy^{\prime }-y=x^{2}\sin x \]
Linear first order, exact, separable. \(y^{\prime }-\frac {y}{x}=x\sin x\), integrating factor \(\mu =e^{\int -\frac {1}{x}dx}=e^{-\ln x}=\frac {1}{x}\), hence\begin {align*} d\left (\mu y\right ) & =\mu \sin x\\ \frac {1}{x}y & =\int \sin xdx+C\\ y & =x\left (C-\cos x\right ) \end {align*}
Verification