Math Problem Statement
selesaikan persamaan diferensial berikut: (D^2 + 2D - 3)= f(x) dengan f(x) = (x^2 + x- 3) + e^x + xe^x + (2xsin(3x) + cos(3x)) - xe^(-2x) sin(x)
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Homogeneous and Non-Homogeneous Differential Equations
Characteristic Equations
Particular Solutions
Formulas
(D^2 + 2D - 3)y = f(x)
Characteristic equation: r^2 + 2r - 3 = 0
Particular solutions based on f(x) components
Theorems
Superposition Principle for Linear Differential Equations
Method of Undetermined Coefficients
Suitable Grade Level
College Level or Advanced High School (Grades 11-12)
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