1. Find a PDE whose solution is z = f(x² + y²) 2. Find a PDE satisfied by z = f(x)g(y)
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Step 1:** For the first PDE where z = f(x² + y²), we have: ∂z/∂x = 2x * ∂f/∂u ∂z/∂y = 2y * ∂f/∂u By eliminating f(u), we get: 2x * ∂z/∂x + 2y * ∂z/∂y = 0 ** Show more…
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