Find the general solution of the following PDE $$x\,\partial_xw - y\,\partial_yw = 0 .$$
Can someone help me with this
I tried it and I get $$C1=(y/x)$$ meaning $$F(w1) = F(y/x)$$but when I try to verify the answer I dont get the null answer as required
Solved
The characteristic method yields $$ \frac{dx}{x}=-\frac{dy}{y} $$ and so, the right answer is $$ xy=C. $$ Then, if you write $u=u(xy)$, you should be able to see that this solves the equation.