(Solved): Solve the differential equation in partial derivatives in the following exercises: \( \frac{\parti ...

Solve the differential equation in partial derivatives in the following exercises: \( \frac{\partial^{2} u}{\partial x \partial y}+2 y \frac{\partial u}{\partial x}=4 x y \) - \( x \frac{\partial u}{\partial x}+u=4 y e^{2 x} \) Note: be detailed in the development of the problem, applying all the steps.