Non-linear second order ODE Watch

Ano123
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Find the general solution of the differential equation
 \displaystyle y^2 \frac{d^2y}{dx^2}+y\left (\frac{dy}{dx} \right )^2 + 2y^2 \frac{dy}{dx} + y^2=0

in the form  y=f(x) .

Any ideas?
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ghostwalker
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(Original post by Ano123)
Find the general solution of the differential equation
 \displaystyle y^2 \frac{d^2y}{dx^2}+y\left (\frac{dy}{dx} \right )^2 + 2y^2 \frac{dy}{dx} + y^2=0

in the form  y=f(x) .

Any ideas?
Extract the factor "y", (y=0 is a solution)

From a bit of playing, what's left can be written in the form:

(yy'+y^2)'+y=0

Any use?
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Ano123
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(Original post by ghostwalker)
Extract the factor "y", (y=0 is a solution)

From a bit of playing, what's left can be written in the form:

(yy'+y^2)'+y=0

Any use?
Nice spot. You must be an expert .
I made the sub  y^2 = z and it all works nicely. Thanks.
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