Looking for Nonlinear 2nd Order DE with Known Solution?

elegysix
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Hello,
Does anyone know of a nonlinear 2nd order DE which must be solved numerically?

I've got a new idea about how tackle it analytically...

So I need one with a known solution to check my results.thanks!
 
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elegysix said:
Hello,
Does anyone know of a nonlinear 2nd order DE which must be solved numerically?

I've got a new idea about how tackle it analytically...

So I need one with a known solution to check my results.


thanks!

The Bernoulli and the Riccati equations are non-linear PDE that can be analytically solved
.
 
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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