| Résoudre sur {\mathbb{R}^{+*}\times\mathbb{R}^{+*}} l’équation {(E)}: {xy^3\dfrac{\partial^2f}{\partial x^2}-yx^3\dfrac{\partial^2f}{\partial y^2}-y^3\dfrac{\partial f}{\partial x}+x^3\dfrac{\partial f}{\partial y}=0}On utilisera le changement {\begin{cases}u=x^2+y^2\cr v=x^2-y^2\end{cases}} |