Partial Differential Equations 1

Calculus Level 4

Solve 2zxy=x2y\frac{{\partial}^{2} z}{\partial x \partial y} = {x}^{2} y given the conditions z(x,0)=x2z(x,0)={x}^{2} and z(1,y)=cosyz(1,y) = \cos {y} .

The solution is of the form z(x,y)=Ax3y2+BcosyCy2+Dx21.z(x,y) = A{x}^{3} {y}^{2} + B \cos {y} - C{y}^{2} +D{x}^{2} -1. What is A+B+C+DA + B + C + D?

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