Question

Find the explicit particular solution to the initial value problem

dy/dx = ye^x ,  y(0) = 2e.

Answer 1

This is a separable equation, and we can rewrite it as:

dy/y = e^xdx.

Taking the antiderivative of both sides we get: 

Exponentiating both sides we get:

 

If we plug in y(0) = 2_e and solve for C we get:

 

So, we can see C=2, and the solution to the initial value problem is: