In 8–11, write the given higher-order equation or system

Chapter 5, Problem 8RP

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QUESTION:

In Problems 8–11, write the given higher-order equation or system in an equivalent normal form (compare Section 5.3).

                               \(2 y^{\prime \prime}-t y^{\prime}+8 y=\sin t\)

Equation Transcription:

Text Transcription:

2y''-ty'+8y=sin⁡ t

Questions & Answers

QUESTION:

In Problems 8–11, write the given higher-order equation or system in an equivalent normal form (compare Section 5.3).

                               \(2 y^{\prime \prime}-t y^{\prime}+8 y=\sin t\)

Equation Transcription:

Text Transcription:

2y''-ty'+8y=sin⁡ t

ANSWER:

Solution. Our aim is to write the given differential system into an equivalent normal form.

................................... (1)

Step 1. We first express the differential equation in the below form.

........................ (2)

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