Find the general solution to a second-order linear non-homogeneous differential equation using the method of undetermined coefficients.

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Solving a Second-Order Non-Homogeneous ODE with Undetermined Coefficients

Parametric equations and vector functions core

Solve \( y'' + y' - 12y = xe^x \).

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What you need first

Solving quadratic equations
The product rule for differentiation
Equating coefficients of polynomials

What this problem tests

Tests the ability to find the characteristic roots for the homogeneous part and correctly apply the method of undetermined coefficients for the non-homogeneous part.

This is a standard problem in an introductory differential equations course or a Calculus II/III course covering ODEs.

Solving a Second-Order Non-Homogeneous ODE with Undetermined Coefficients

What you need first

What this problem tests

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