exo7 5898

$2 \frac{\partial f}{\partial x}- \frac{\partial f}{\partial y}= 0$ en posant $u = x+y$ et $v = x+2y$.

$x \frac{\partial f}{\partial y}-y \frac{\partial f}{\partial x}=0$ sur $\Rr^2\setminus\{(0,0)\}$ en passant en polaires.

$x^2 \frac{\partial^2f}{\partial x^2}+2xy \frac{\partial^2f}{\partial x\partial y}+y^2 \frac{\partial^2f}{\partial y^2}= 0$ sur $]0, +\infty[\times\Rr$ en posant $x = u$ et $y = uv$.