Explanation Formula used: The Wronskian of any two solutions y 1 and y 2 to the equation y ″ ( t ) + p y ′ ( t ) + q y ( t ) = 0 on ( a , b ) is given by Abel’s formula W [ y 1 , y 2 ] ( t ) = C exp { − ∫ t 0 t p ( τ ) d τ } . Calculation: The given differential equation is, t y ″ + ( t − 1 ) y ′ + 3 y = 0 . Divide by t and simplify as, y ″ + ( t − 1 t ) y ′ + 3 t y = 0 y ″ + ( 1 − 1 t ) y ′ + 3 t y = 0 Comparing y ″ + ( 1 − 1 t ) y ′ + 3 t y = 0 with the general form y ″ ( t ) + p y ′ ( t ) + q y ( t ) = 0 gives p = 1 − 1 t

Fundamentals of Differential Equations (9th Edition)

9th Edition

ISBN: 9780321977069

Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Publisher: PEARSON

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 4.7, Problem 33E

To determine

The Wronskian of two solutions on (0,∞) to ty″+(t−1)y′+3y=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.7, Problem 32E

Chapter 4.7, Problem 34E

Students have asked these similar questions

12. Compute the Gradient of the Scalar Field Go to page 38 of the linked document for the scalar field problem. Find the gradient of the scalar field and interpret its meaning. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide a clear explanation of the steps involved.

Mercedes-Benz stadium's soccer field is 115 yards in length × 75 yards in width. When Mercedes-Benz hosts a concert, the stage takes up the first 20 yds. The two VIP areas takes up the next 4 yards. After that, there are six ground floor sections. Each ground floor section is divided by aisles that are 5 yards wide. Each chair requires a square of 1 yard x 1 yard. Use the above information to answer the following questions: How many VIP ground tickets could you sell? How many additional ground tickets could you sell?

4. Find the Inverse of the Function Check page 42 of the document for the problem involving the inverse function. Find the inverse of the given function and check if it satisfies the original equation. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Explain each step thoroughly.

Chapter 4 Solutions

Fundamentals of Differential Equations (9th Edition)

Ch. 4.1 - Verify that for b = 0 and Fext(t) = 0, equation...Ch. 4.1 - If Fext(t) = 0, equation (3) becomes my + by + ky...Ch. 4.1 - Show that if Fext(t) = 0, m = 1, k = 9, and b = 6,...Ch. 4.1 - Verify that y = sin 3t + 2 cos 3t is a solution to...Ch. 4.1 - Prob. 5E Ch. 4.1 - An external force F(t) = 2 cos 2t is applied to a...Ch. 4.1 - Prob. 7E Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - Prob. 10E

Knowledge Booster

$Advanced Math$

Learn more about

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

The Wronskian of two solutions on ( 0 , ∞ ) to t y ″ + ( t − 1 ) y ′ + 3 y = 0 .

Solution Summary: The author explains how the Wronskian of two solutions on (0,infty) is divided by t and simplified by Abel’s formula.

Concept explainers

Videos

The Wronskian of two solutions on (0,∞) to ty″+(t−1)y′+3y=0.

Want to see the full answer?

Chapter 4 Solutions