Solution Found!
Ch 4.1 - 35E
Chapter 4, Problem 35E(choose chapter or problem)
(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 .