Solution Found!
Show that the three solutions and to are linearly
Chapter 4, Problem 4E(choose chapter or problem)
Show that the three solutions \(1 / 1(1-t)^{2}\), \(1 /(2-t)^{2}\) and \(1 /(3-t)^{2}\) to \(y^{\prime \prime}-6 y^{2}=0\) are linearly independent on \((-1,1)\). (See Problem 35, Exercises , page 166.)
Equation Transcription:
Text Transcription:
1/1(1-t)^2
1/(2-t)^2
1/(3-t)^2
y"-6y^{2}=0
(-1,1)
Questions & Answers
QUESTION:
Show that the three solutions \(1 / 1(1-t)^{2}\), \(1 /(2-t)^{2}\) and \(1 /(3-t)^{2}\) to \(y^{\prime \prime}-6 y^{2}=0\) are linearly independent on \((-1,1)\). (See Problem 35, Exercises , page 166.)
Equation Transcription:
Text Transcription:
1/1(1-t)^2
1/(2-t)^2
1/(3-t)^2
y"-6y^{2}=0
(-1,1)
ANSWER:
Solution :
Step 1 :
In this problem we have to show that the given three solutions of differential equation are linearly independent.
Given solutions are
This solutions are linear combination on (-1,1)