Solve the initial value problem...?

Question

dy/dx = 12 sin^2 x cos x, y(0)=4

Answer 1

dy/dx=12 sin²x cos x

Multiply each side by 'dx'.

dy = (12 sin²x cos x)dx

Apply integral each side.

Integrals with Trigonometric Functions formula: 

Given that y(0) = 4.

4 = 4[sin(0)]³ + c

4 = 0 + c

Therefore c = 4

y = 4(sin³x) + 4.