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

Can you explain how the error term in the CF Algorithm relates to the (m+1)th complete quotient? Also, what would be a good way to explain the connection between these two slides? How can one transition between them for a presentation?

How can I explain the pi example in a presentation? I'm having trouble transitioning between these two slides

McGilla Golf has decided to sell a new line of golf clubs. The clubs will sell for $895 per set and have a variable cost of $431 per set. The company has spent $200,000 for a marketing study that determined the company will sell 80,000 sets per year for seven years. The marketing study also determined that the company will lose sales of 8,600 sets per year of its high-priced clubs. The high-priced clubs sell at $1,325 and have variable costs of $645. The company will also increase sales of its cheap clubs by 10,800 sets per year. The cheap clubs sell for $340 and have variable costs of $141 per set. The fixed costs each year will be $14,350,000. The company has also spent $1,500,000 on research and development for the new clubs. The plant and equipment required will cost $43,700,000 and will be depreciated on a straight-line basis. The new clubs will also require an increase in net working capital of $3,625,000 that will be returned at the end of the project. The tax rate is 25…

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,∞).