Solve the given differential equation by separation of varia

Solve the given differential equation by separation of variables. dy/dx = sin 4x

Solution

dy/dx = sin(4x)

dy = sin(4x)*dx

Integrating both sides :

u = 4x
du = 4*dx
du/4 = dx

So, y = (integral) sin(u)*du/4

y = (1/4)*(-cos(u)) + C

y = (-1/4)cos(4x) + C ---> ANSWER