Find a solution to the following initial-value problem: dy dx = y(y − 2)e x , y (0) = 1.

This equation is separable, as

Integrate both sides; on the left, expand the fraction as

Then

Since , we get

so that the particular solution is

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

there are infinitely many solutions.