# Find the general solution of the pde $𝑢𝑢_{xy} + 𝑢_𝑥𝑢_𝑦 = 0$

Find the general solution of the partial differential equation

$$𝑢𝑢_{xy} + 𝑢_𝑥𝑢_𝑦 = 0$$.

This is a second order quasilinear equation, it cannot be solved using the method of characteristics. Does it have another way to find the general solution?

$$\left(uu_{x}\right)_{y}=uu_{xy}+u_{x}u_{y}$$
$$\left(\dfrac{1}{2}u^{2}\right)_{x}=uu_{x}$$