Solve the differential equation dy/dx = y sin 2x, given that y(0) = 1. ​

Question

Solve the differential equation \(\frac{dy}{dx}\) = y sin 2x, given that y(0) = 1.

Answer 1

We have,

\(\frac{dy}{dx}\) = y sin 2x

⇒ \(\frac{dy}{y}\) = y sin2x

⇒ log y = - \(\frac{cos2x}2\) + c

For y =1, x = 0, we have,

c = \(\frac{1}{2}\)

⇒ log y = \(\frac{1}{2}\)(1 - cos2x)

⇒ log y = sin²x

Thus, 

The particular solution is:

y = e^sin2x