Sorry I don't quite understand the relation, but my attempt on continuing the question with your hint:
\begin{aligned}\sqrt {\dfrac {\partial z}{\partial x}}+\sqrt {\dfrac {\partial z}{\partial y}}=x\\
\sqrt {\dfrac {\partial z}{\partial x}}=x\ & \sqrt {\dfrac {\partial z}{\partial y}}=0\\...
Thank you for your reply, my attempt to your problem are as follow:
\begin{aligned}\dfrac {\partial z}{\partial x}=x^{2}\\ \partial z=x^{2}\partial x\\ z=\dfrac {x^{3}}{3}+c\end{aligned}
My attempt to my problem are as follow:
I try to reproduce the equation to a 1st order differential equation...
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Hi everyone,
I have encountered a partial differential equation with square roots which I don't have a clue in solving it. After letting z=F(x)+G(y), I can't really figure out the next step. I tried squaring both sides but...