Explanation Given: The equations is y ″ + ( x 2 − 1 ) y = 0 Approach: 1) Suppose that ϕ 1 and ϕ 2 are nontrivial solutions to the differential equations y ″ + Q 1 ( x ) y = 0 y ″ + Q 2 ( x ) y = 0 respectively on ( a , b ) . If Q 2 ( x ) ≥ Q 1 ( x ) for x in ( a , b ) then between any two consecutive zeroes x 1 and x 2 of ϕ 1 there exists a zero of ϕ 2 unless Q 2 ( x ) = Q 1 ( x ) on [ x 1 , x 2 ] and ϕ 1 and ϕ 2 are linearly dependent on [ x 1 , x 2 ] . 2) If Q ( x ) ≤ 0 on [ a , b ] , then a nontrivial solution to y ″ + Q ( x ) y = 0 has at most one zero in [ a , b ] . Calculation: Consider the equations y ″ + y = 0 ..

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 11.8, Problem 6E

To determine

To prove:

A nontrivial solution to y″+(x2−1)y=0 has at most one zero in (−1,1) and has infinitely many zeroes in (−∞,−1) and (1,∞).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.8, Problem 4E

Chapter 11.8, Problem 7E

Students have asked these similar questions

In a survey, the planning value for the population proportion is p 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.03? Round your answer up to the next whole number. 800 {

Q/ calculate the Fourier series of f(x) on the given interval f(x) = x Sin X 9 -

Q 2/ Calculate the Fourier series of f(x) on the given interval f(x) = x Sin X - 16 x ≤ メ

Chapter 11 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 3E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 7E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 9E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To prove: A nontrivial solution to y ″ + ( x 2 − 1 ) y = 0 has at most one zero in ( − 1 , 1 ) and has infinitely many zeroes in ( − ∞ , − 1 ) and ( 1 , ∞ ) .

Solution Summary: The author explains that a nontrivial solution to y′′+(x2-1)y=0 has at most one zero and infinitely many zeroes

Concept explainers

Videos

To prove:

A nontrivial solution to y″+(x2−1)y=0 has at most one zero in (−1,1) and has infinitely many zeroes in (−∞,−1) and (1,∞).

Want to see the full answer?

Chapter 11 Solutions

To prove: A nontrivial solution to y ″ + ( x 2 − 1 ) y = 0 has at most one zero in ( − 1 , 1 ) and has infinitely many zeroes in ( − ∞ , − 1 ) and ( 1 , ∞ ) .

Solution Summary: The author explains that a nontrivial solution to y′′+(x2-1)y=0 has at most one zero and infinitely many zeroes

Concept explainers

Videos

To prove: A nontrivial solution to y″+(x2−1)y=0 has at most one zero in (−1,1) and has infinitely many zeroes in (−∞,−1) and (1,∞).

Want to see the full answer?

Chapter 11 Solutions

To prove:

A nontrivial solution to y″+(x2−1)y=0 has at most one zero in (−1,1) and has infinitely many zeroes in (−∞,−1) and (1,∞).