The transformed equation of $\frac{\mathrm{dy}}{\mathrm{dx}}-\mathrm{y} \mathrm{tanx}=\frac{\mathrm{sinx}.{\cos }^2\mathrm{x}}{{\mathrm{y}}^2}$

$\begin{array}{l}Given{y}^2\frac{dy}{dx}-y^{3}Tanx=\sin x{\cos }^{2}x\\ Let{y}^3=z\\ 3y^2\frac{dy}{dx}=\frac{dz}{dx}\\ y^2\frac{dy}{dx}=\frac{dz}{dx}\\ y^2\frac{dy}{dx}=\frac{1}{3}\frac{dz}{dx}\\ \Rightarrow \frac{1}{3}\frac{dz}{dx}-zTanx=\sin x{\cos }^{2}x\\ \Rightarrow \frac{dz}{dx}-3zTanx=3\sin x{\cos }^{2}x\end{array}$