xy''+2y'=x(y')^2

z=y'

xz'+2z=xz^2

i cant solve it

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- Dec 8th 2010, 04:04 AMtransgalacticz=y' solution
xy''+2y'=x(y')^2

z=y'

xz'+2z=xz^2

i cant solve it - Dec 8th 2010, 04:44 AMProve It

.

This is a Bernoulli Equation, so make the substitution .

Then , so

.

Substituting into the DE gives

.

Now this is First Order Linear, so use the Integrating Factor method.

The Integrating Factor is .

Multiplying through by the Integrating Factor gives

.

Since

.

And finally . You can do this using Partial Fractions.