Question

Find all solutions of y'-xy=(x^3)(y^3).

Answer 1

Its Bernoulli.
Get it into the form of this.
\[\LARGE \frac{dy}{dx} + P(y) = Q\]

Answer 2

Make sure that Q should be solely a function of x.

Answer 3

So do I divided the whole equation by y^3?

Answer 4

yep!

Answer 5

Then what do I do?

Answer 6

sibstitute v = 1/y^2

Answer 7

\[\Large \frac{y'}{y^3}-\frac{x}{y^2}=(x^3)\]
Let v=1/y^2

Answer 8

rationalllllllllllllllll

Answer 9

Let me work it out and I'll tell you what I got.

Answer 10

sure!

Answer 11

Since v=1/y^2, so y=1/sqrt(v), right?