No Time Term in Elliptic PDEs? Confirm Here!

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When looking at Elliptic PDEs that describe a physical system, do these typically not involve a time term?
I have yet to see an elliptic PDE involving a time term, which seem to be associated with parabolic/hyperbolic PDEs rather than elliptic.

Can anyone confirm?
 
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Typically elliptic PDE's are static equations that do not involve a time term. Examples are Laplace's equation or Poisson's equation.
 
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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