Question

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (2) The solution of PDE dz/dx+dz/dy=z^2 is z=-[y+f(x-y) ].

Answer 1

It is false.

If we take $f(u)=0$, then we obtain $z=-y$.

Then $\frac{dz}{dx}=0$, $\frac{dz}{dy}=-1$ and $z^2=y^2$.

Functions $0+(-1)=-1$ and $y^2$ are not equal.