Show that if y(t) satisfies then y(-t) satisfies

Chapter 4, Problem 1E

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QUESTION:

Show that if \(y(t)\) satisfies \(y^{\prime \prime}-t y=0\), then \(y(-t)\) satisfies \(y^{\prime \prime}+t y=0\).

Equation Transcription:

Text Transcription:

y(t)

y"-ty=0

y(-t)

y"+ty=0

Questions & Answers

QUESTION:

Show that if \(y(t)\) satisfies \(y^{\prime \prime}-t y=0\), then \(y(-t)\) satisfies \(y^{\prime \prime}+t y=0\).

Equation Transcription:

Text Transcription:

y(t)

y"-ty=0

y(-t)

y"+ty=0

ANSWER:

SOLUTION
Step 1

Given

  satisfies

We have to prove ,  satisfies the equation

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