# How do you solve #dy/dx = xy^2#?

##### 2 Answers

#### Explanation:

Let's separate our variables, IE, have each side of the equation only in terms of one variable. This entails

Integrate each side:

Note that we would technically have constants of integration on both sides, but we moved them all over to the right and absorbed them into

Now, let's get an explicit solution with

Let's get the fraction out of the denominator. It just looks messy.

Well,

Thus,

where

#### Explanation:

We separate variables:

Now we integrate both sides:

where

Now we solve for

where