Nonlinear second order differential equation

Ioria
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Hello!
It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation:
it's a non-linear second order differential equation.

ay''+b|y|y'+cy+dx=0

Some ideas?
 
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No idea analytically, but have you tried numerically solving it? That way you can get an idea of what it look like and then perhaps asymptotic analysis.

Have you tried writing it as a first order system?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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