DiffEqUndetermined Coefficients

Undetermined Coefficients — Particular Solution

Find yₚ for ay″ + by′ + cy = g(x) by guessing a trial form based on g(x) and solving for undetermined constants.

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Homogeneous Part: ay″ + by′ + cy

a (y″)

b (y′)

c (y)

Forcing function g(x)

Results

Homogeneous Solution yₕ

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Trial Form for yₚ

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Particular Solution yₚ

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General Solution y = yₕ + yₚ

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Step-by-Step Work

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Solution y = yₕ + yₚ (C₁=C₂=1, x∈[0,5])