Find the general solution of the following differential equation: dy/dx = sin^3 x cos^2 x + xe^x ​

Question

Find the general solution of the following differential equation:

\(\frac{dy}{dx}\) = sin³ x cos² x + xe^x

Answer 1

Here we have,

y = ∫(sin³x cos²x + xe^x) dx

⇒ ∫cos²x(1 - cos²x) sin x dx + ∫ xe^x dx

Taking cosx as t we have,

⇒ cos x = t,

⇒ - sin x dx = dt,

So we have,