Ok so basically I have two differential equations:
1) x'' + wx' + w^2 x = sin5t
2) del squared u = 0
The first is obviously just the equation for the driven harmonic oscillator. The second is Laplace's equation.
The question asks: In both cases, is the linearity believed to be exact, or the result of an approximation (if so, say what it is). In the case of a second order PDE what are the properties of solutions that follow when it is (a) linear (b) linear and homogeneous
Is the linearity exact in both cases? im pretty sure it is in the ODE case, right? Is it also in the PDE case (i.e. 2) ? ) when is linearity not exact?
For the second question:
I guess that when the PDE is homogeneous and linear then linear sums of solutions are also solutions, but what about when it is just linear?
... and the ones that won't