Question

What is a solution to the differential equation dy/dx= y^2? (Please)

Answer 1

`y(x)=-1/(x+C)`

Explanation:

This is a separable differential equation. We'll get all `y,dy` on the right side and all `x,dx` on the left.

`dy/dx=y^2`

`1/y^2dy=dx`

Note that we have no `x` so all we do is move `dx` to the left.

`y^-2dy=dx`

Integrate both sides:

`inty^-2dy=intdx`

`-1/y=x+C`

We need an explicit solution in the form `y(x):`

`-1=y(x+C)`

`y(x)=-1/(x+C)`

Answer 2

`y=-1/(x+C)`

Explanation:

`(dy)/dx=y^2`
`y^(-2)dy=dx`
`inty^(-2)dy=intdx`
`-y^(-1)=x+C`
`y^(-1)=-x-C`
`y=1/(-x-C)`
`y=-1/(x+C)`, `C` is a constant