Solution Found!
In 8–11, write the given higher-order equation or system
Chapter 5, Problem 8RP(choose chapter or problem)
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)