solving an equation

[kcoe05]

Alright so I am trying to solve the equation:

dy/dx + y/x = 3y^3

The first thing I did was multiply both sides by x to get:

x (dy/dx) + y = 3xy^3

then i got

xy + y = 3xy^3


then i separated the right side to get:


y( x + 1) = 3xy^3


divide both sides by y

(x + 1) = 3xy^2

can someone tell me if I am going in the right direction or not?

Thanks

 

[pitoten]

An ordinary differential equation of the form y'+ P(x)y = Q(x)y^n is called a Bernoulli equation. You must find the integrating factor
M(x) by using the proper u substitution.

In your case:

P(x) = 1/x
Q(x) = 3
n = 3

Try u = 1/(y^2).

Also check out the wikipedia site on Bernoulli equs.