User:Egm6321.f12.team4.harris/Homework56 R*6.6 Part 2.6

Problem R*6.6 2.6 – Particular Solution
sec33-5

Statement
Deduce the particular solution $$ y_p(t) $$ for a general excitation $$ f(t) $$.

Solution
Given the equation
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$$ y(t)=e^{-\beta t} \int ^t (\frac{e^{(\beta - \alpha)s}}{\bar {a_1}} \int ^s (e^{\alpha t} f(t)dt))ds + e^{-\beta t} \int ^t kds $$     (6.6.?)
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one can deduce that the particular solution $$ y_p(t) $$ is the portion of equation 6.6.? that includes
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$$ y_p(t)=e^{-\beta t} \int ^t (\frac{e^{(\beta - \alpha)s}}{\bar {a_1}} \int ^s (e^{\alpha t} f(t)dt))ds $$     (6.6.?)
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The remaining portion would be the homogeneous solution.