Solution Found!
(a) Use the energy integral lemma to derive the family of
Chapter 4, Problem 5E(choose chapter or problem)
(a) Use the energy integral lemma to derive the family of solutions \(y(t)=1 /(t-c)\) to the equation \(y^{\prime \prime}=2 y^{3}\).
(b) For \(c \neq 0\) show that these solutions are pairwise linearly independent for different values of in an appropriate interval around \(c \neq 0\).
(c) Show that none of these solutions satisfies the initial conditions \(y(0)=1\), \(y^{\prime}(0)=2\).
Equation Transcription:
Text Transcription:
y(t)=1/(t-c)
y"=2y^3
C not= 0
t-0
y(0)=1
y'(0)=2
Questions & Answers
QUESTION:
(a) Use the energy integral lemma to derive the family of solutions \(y(t)=1 /(t-c)\) to the equation \(y^{\prime \prime}=2 y^{3}\).
(b) For \(c \neq 0\) show that these solutions are pairwise linearly independent for different values of in an appropriate interval around \(c \neq 0\).
(c) Show that none of these solutions satisfies the initial conditions \(y(0)=1\), \(y^{\prime}(0)=2\).
Equation Transcription:
Text Transcription:
y(t)=1/(t-c)
y"=2y^3
C not= 0
t-0
y(0)=1
y'(0)=2
ANSWER:
Solution
Step 1
In this problem, we have to derive the family of solution to the equation
.
b) We have to show that pairwise solution is linearly independent.
c) We have to check the initial conditions whether it satisfies by the solution or not.