# What is the general solution of the differential equation  dy/dx = 8sin2x ?

Oct 6, 2017

$y = C - 4 \cos 2 x$

#### Explanation:

We have:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 8 \sin 2 x$

This is a separable ODE, do we can "separate the variables" to give:

$\int \setminus \mathrm{dy} = \int \setminus 8 \sin 2 x \setminus \mathrm{dx}$

Both integrals are of standard functions, so we can now integrate to get the General Solution:

$y = - \frac{8 \cos 2 x}{2} + C$

$\therefore y = - 4 \cos 2 x + C$

$\therefore y = C - 4 \cos 2 x$