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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.

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

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

Do you mean $x\,\frac{{dy}} {{dx}} = y + xy^2$?

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

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• 5 weeks later...

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.

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