What is the class of this equation?

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Hi all,

Please tell me the class of this equation, and if possible how to solve this kind of equations:

\Deltau(\vec{r})=F(u(\vec{r}),\vec{r})


Thanks in advance.
 
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3D 2nd order non-linear - no 1st order term.
IIRC: There are no general approaches for solving this type of equation.
The trouble is that the RHS function can be ANYTHING.
 
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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