I know i can't change the title but i solved the problem i was looking for originally and need help with another...

 

The question says to use an integrating factor to solve:

 

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

 

The problem comes at the very last part to find v' and v because of the y^2 term.

 

The factor i'm using is: y = v*exp(-integral[-1/x]dx) where the -1/x is the term infront of the y when you divide by x and bring it across.

 

Any pointers would be great. Thanks.

I don't know the answer but a google search got me to this!

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

Do you mean [math]x\,\frac{{dy}}

{{dx}} = y + xy^2[/math]?

 

This is not a linear ODE, so you can't solve it with integratin' factor method. This is actually a Bernoulli's Differential Equation.

The hint to solution is the following:

 

Substitute y from both sides of the equation, devide everything by x*y and look carefully on the left hand side of this equation.