Math Problem Statement
Find the cf of (D^2 + D + 1)y = 1 + x^2 + x^3
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Complementary Function
Quadratic Equations
Complex Roots
Formulas
Characteristic equation: r^2 + r + 1 = 0
Quadratic formula: r = (-b ± √(b^2 - 4ac)) / 2a
Complementary function (CF): y_c = e^(αx) (C1 cos(βx) + C2 sin(βx))
Theorems
Quadratic Formula
Solutions to homogeneous differential equations with complex roots
Suitable Grade Level
Grades 11-12, Undergraduate
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