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

[Squizzel]

Homework Statement

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

Homework Equations

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

 

[STEMucator]

Homework Statement

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

Homework Equations

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]

Homework Statement

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

Homework Equations

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 .