Soit \(f : {\R^2} \to \R\) de classe \(\mathcal{C}^2\) et \(g(u,v) = f(uv,u+v)\).
1
Calculer \(\frac{\partial^2 g}{\partial u \partial v}\).
2
Résoudre l’équation : \(x\frac{\partial^2 f}{\partial x^2} + y\frac{\partial^2 f}{\partial x \partial y} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial f}{\partial x} = y\).