Questions on "Partial Differential Equations", as opposed to "ordinary differential equations".

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Solutions to the PDE :$2V\frac{\partial I}{\partial V}+2W\frac{\partial I}{\partial W}=I$

While working on engineering problem, I came across this PDE: Let $c_1,c_2$ be two real numbers. Find a continuous function $I:\mathbb{R}_{\geq 0}\times\mathbb{R}_{\geq 0}\rightarrow \mathbb{R}$ such ...