General solution of the differential equation $\sin ^3 \mathrm{x} \frac{\mathrm{dx}}{\mathrm{dy}}=\sin \mathrm{y}$ is given by

Question

Aicharya · Accepted Answer

$\begin{aligned} & \sin ^3 x \frac{d x}{d y}=\sin y \Rightarrow \int \sin ^3 x d x=\int \sin y d y \ & \Rightarrow \int \frac{3 \sin x-\sin 3 x}{4} d x=\int \sin y d y \ & \Rightarrow \frac{-3}{4} \cos x+\frac{1}{4} \cdot \frac{\cos 3 x}{3}=-\cos y+C \ & \Rightarrow \cos y-\frac{3}{4} \cos x+\frac{1}{12} \cos 3 x=C\end{aligned}$

General solution of the differential equation $\sin ^3 \mathrm{x} \frac{\mathrm{dx}}{\mathrm{dy}}=\sin…

Solution