Question

Solve the DiffEQ (y^2+xy^2)y'=1

Answer 1

This equation is separable. Separate and integrate.

Answer 2

Tried to split don't know how to deal with y^2dy/dx+xy^2dy/dx

Answer 3

unless I can change the equation to y^2+xy^2= dx/dy...

Answer 4

Think for a minute.

You want to write y^2 + xy^2 as the product of a function in y and a function in x.

How can you factorize this expression in order to do so?

Answer 5

2y^2dy=dx/x?

Answer 6

No, that simply can't be right by basic algebra.

Factorize y^2 + xy^2 for me.

Answer 7

(x+1)y^2?

Answer 8

Yes ... hence .... now separating, you have ... what?

Answer 9

What do I do with the y'?

Answer 10

(x+1)y^2 dy/dx = 1.

Therefore

y^2 dy = dx / (x + 1)

Answer 11

Oh I see.