# What kind of problem is this. (Seperable or Bernoullis) / Diff EQ

## Homework Statement

xy^2 dy/dx = y^3 - x^3 , y(1) = 2

## The Attempt at a Solution

It says to solve the initial value problem. I am assuming it is not a Bernoulli, but I can't seem to separate it. What should I do?

Thanks

This is what I get when I separate it, is this right?

y^2-y^3 dy = -x^2 dx

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Zondrina
Homework Helper

## Homework Statement

xy^2 dy/dx = y^3 - x^3 , y(1) = 2

## The Attempt at a Solution

It says to solve the initial value problem. I am assuming it is not a Bernoulli, but I can't seem to separate it. What should I do?

Thanks

This is what I get when I separate it, is this right?

y^2-y^3 dy = -x^2 dx
xy^2 dy/dx = y^3 - x^3
dy/dx = y/x - x^2/y^2

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

xy^2 dy/dx = y^3 - x^3 , y(1) = 2

## The Attempt at a Solution

It says to solve the initial value problem. I am assuming it is not a Bernoulli, but I can't seem to separate it. What should I do?

Thanks

This is what I get when I separate it, is this right?

y^2-y^3 dy = -x^2 dx
How do you get that last line?

It should be y2 dx - y3 dy = -x2 dx, which is not separated.

Try the substitution, y = xv .