xy''+2y'=x(y')^2
z=y'
xz'+2z=xz^2
i cant solve it
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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.