Ch 4.1 - 35E

Chapter 4, Problem 35E

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QUESTION:

(a) Verify that \(y_{p_{1}}=3 e^{2 x} \text { and } y_{p_{2}}=x^{2}+3 x\) are, respectively, particular solutions of \(y^{\prime \prime}-6 y^{\prime}+5 y=-9 e^{2 x}\) and \(y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16\).

(b) Use part (a) to find particular solutions o \(y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16-9 e^{2 x}\) and \(y^{\prime \prime}-6 y^{\prime}+5 y=-10 x^{2}-6 x+32+e^{2 x}\).

Text Transcription:

y_{p_{1}}=3 e^{2 x} \text { and } y_{p_{2}}=x^{2}+3 x

y^{\prime \prime}-6 y^{\prime}+5 y=-9 e^{2 x}

y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16

y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16-9 e^{2 x}

y^{\prime \prime}-6 y^{\prime}+5 y=-10 x^{2}-6 x+32+e^{2 x}

Questions & Answers

QUESTION:

(a) Verify that \(y_{p_{1}}=3 e^{2 x} \text { and } y_{p_{2}}=x^{2}+3 x\) are, respectively, particular solutions of \(y^{\prime \prime}-6 y^{\prime}+5 y=-9 e^{2 x}\) and \(y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16\).

(b) Use part (a) to find particular solutions o \(y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16-9 e^{2 x}\) and \(y^{\prime \prime}-6 y^{\prime}+5 y=-10 x^{2}-6 x+32+e^{2 x}\).

Text Transcription:

y_{p_{1}}=3 e^{2 x} \text { and } y_{p_{2}}=x^{2}+3 x

y^{\prime \prime}-6 y^{\prime}+5 y=-9 e^{2 x}

y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16

y^{\prime \prime}-6 y^{\prime}+5 y=5 x^{2}+3 x-16-9 e^{2 x}

y^{\prime \prime}-6 y^{\prime}+5 y=-10 x^{2}-6 x+32+e^{2 x}

ANSWER:

Step 1 of 5

In this problem we have to verify that  is the particular solution of the nonhomogeneous differential equation  , and  is  particular solution of the nonhomogeneous differential equation .

 

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