Understanding Non-Linear PDEs: Causes and Implications

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What makes a PDE non-linear please?

Thanks!
 
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Do you know what makes an ordinary diff. eq. non-linear?
 
Do you know what nonlinear means? :)
 
Having a non-linear function of the dependent function anywhere in the equation. I suspect arildno and Tide were wondering how you could be studying partial differential equations if you don't know what "non-linear" means!
 
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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