Solve the following differential equations: (sin x)dy/dx + y cos x = 2 sin^2 x cos x

Question

Solve the following differential equations:

\((sin\,x)\frac{dy}{dx}+y\,cos\,x=2\,sin^2x\,cos\,x\)

Answer 1

This is a first order linear differential equation of the form

The integrating factor (I.F) of this differential equation is,

Hence, the solution of the differential equation is,

⇒ cosxdx = dt [Differentiating both sides]

By substituting this in the above integral, we get

Thus, the solution of the given differential equation is \(y = \frac{2}{3}sin^2x + c\,cosec\,x\)