Question Number 214678 by issac last updated on 16/Dec/24
$$\mathrm{solve} \\ $$$$\mathrm{partial}\:\mathrm{differantial}\:\mathrm{equation} \\ $$$${x}\frac{\partial{f}\left({x},{y}\right)}{\partial{x}}+{y}\frac{\partial{f}\left({x},{y}\right)}{\partial{y}}={f}\left({x},{y}\right)\mathrm{ln}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right) \\ $$$$\frac{\partial^{\mathrm{2}} {f}\left({x},{y}\right)}{\partial{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {f}\left({x},{y}\right)}{\partial{y}^{\mathrm{2}} }=\mathrm{0} \\ $$