Use the variation of parameters formula (10) to derive a

Chapter 9, Problem 31E

(choose chapter or problem)

Use the variation of parameters formula (10) to derive a formula for a particular solution \(y_{p}\) to the scalar equation \(y^{\prime \prime}+p(t) y^{\prime}+q(t) y=g(t)\) in terms of two linearly independent solutions \(y_{1}(t), y_{2}(t)\) of the corresponding homogeneous equation. Show that your answer agrees with the formulas derived in Section 4.6. [Hint: First write the scalar equation in system form.]

Equation Transcription:

Text Transcription:

yp

y''+p(t)y'+q(t)y=g(t)

y1(t),y2(t)

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