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4. Find a general solution for the given differential
Chapter 6, Problem 4RP(choose chapter or problem)
Find a general solution for the given differential equation.
(a) \(y^{(4)}+2 y^{\prime \prime \prime}-4 y^{\prime \prime}-2 y^{\prime}+3 y=0\)
(b) \(y^{\prime \prime}+3 y^{\prime \prime}-5 y^{\prime}+y=0\)
(c) \(y^{(5)}-y^{(4)}+2 y^{\prime \prime}-2 y^{\prime \prime}+y^{\prime}-y=0\)
(d) \(y^{\prime \prime \prime}-2 y^{\prime \prime}-y^{\prime}+2 y=e^{x}+x\)
Equation transcription:
Text transcription:
y^{(4)}+2 y^{prime prime prime}-4 y^{prime prime}-2 y^{prime}+3 y=0
y^{prime prime}+3 y^{prime prime}-5 y^{prime}+y=0
y^{(5)}-y^{(4)}+2 y^{prime prime}-2 y^{prime prime}+y^{prime}-y=0
y^{prime prime prime}-2 y^{prime prime}-y^{prime}+2 y=e^{x}+x
Questions & Answers
QUESTION:
Find a general solution for the given differential equation.
(a) \(y^{(4)}+2 y^{\prime \prime \prime}-4 y^{\prime \prime}-2 y^{\prime}+3 y=0\)
(b) \(y^{\prime \prime}+3 y^{\prime \prime}-5 y^{\prime}+y=0\)
(c) \(y^{(5)}-y^{(4)}+2 y^{\prime \prime}-2 y^{\prime \prime}+y^{\prime}-y=0\)
(d) \(y^{\prime \prime \prime}-2 y^{\prime \prime}-y^{\prime}+2 y=e^{x}+x\)
Equation transcription:
Text transcription:
y^{(4)}+2 y^{prime prime prime}-4 y^{prime prime}-2 y^{prime}+3 y=0
y^{prime prime}+3 y^{prime prime}-5 y^{prime}+y=0
y^{(5)}-y^{(4)}+2 y^{prime prime}-2 y^{prime prime}+y^{prime}-y=0
y^{prime prime prime}-2 y^{prime prime}-y^{prime}+2 y=e^{x}+x
ANSWER:Solution
Step 1
In this problem, we have to find the solution of differential equation.