# Partial Differential Equations 1

Calculus Level 4

Solve $\frac{{\partial}^{2} z}{\partial x \partial y} = {x}^{2} y$ given the conditions $$z(x,0)={x}^{2}$$ and $$z(1,y) = \cos {y}$$.

The solution is of the form $z(x,y) = A{x}^{3} {y}^{2} + B \cos {y} - C{y}^{2} +D{x}^{2} -1.$ What is $$A + B + C + D$$?

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