Math Problem Statement
solve the recurrenece relation an=5an-1-4an-2+n^2 where a1=1,a2=2
Solution
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Math Problem Analysis
Mathematical Concepts
Recurrence Relations
Homogeneous and Non-Homogeneous Equations
Characteristic Equations
Formulas
an = 5a(n-1) - 4a(n-2) + n^2
Characteristic Equation: r^2 - 5r + 4 = 0
General Solution: an = C1 + C2 * 4^n + An^2 + Bn + C
Theorems
Characteristic Equation Theorem
Method of Undetermined Coefficients
Suitable Grade Level
Undergraduate level or Advanced High School (Grades 11-12)