Math Problem Statement

Solve the differential equation D^2 - DD - 2D + 2D + 2D] z = e^(2x+3y) + sin(sin(2x + y)) + xy

Solution

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Math Problem Analysis

Mathematical Concepts

Differential Equations
Linear Operators
Second-Order PDEs
Exponential Functions

Formulas

D^n z = f(x, y)
General solution form for second-order linear PDEs
Solution of the form z = f1(y - x) + e^(-2x)f2(y - x)

Theorems

Superposition principle for linear PDEs
Separation of variables method

Suitable Grade Level

University (Advanced)

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