📘 multivariable calculus

1. **Problem 1:** Given $z=x^3 + y^3 - 3x^2y$, verify $x^2 \frac{\partial^2 z}{\partial x^2} + 2xy \frac{\partial^2 z}{\partial x \partial y} + y^2 \frac{\partial^2 z}{\partial y^2

1. **State the problem:** We have a function of two variables: $$u(x_1, x_2) = 2 x_2$$.