Explanation The given differential equation is 2 t 2 y ″ − 5 t y ′ + 5 y = 0 , t > 0 . Rewrite the given differential equation in the standard form. 2 t 2 y ″ − 5 t y ′ + 5 y = 0 2 2 t 2 y ″ − 5 2 t y ′ + 5 2 y = 0 2 t 2 y ″ − 5 2 t y ′ + 5 2 y = 0 Compare t 2 y ″ − 5 2 t y ′ + 5 2 y = 0 with general form t 2 y ″ + α t y ′ + β y = 0 . Here, α = − 5 2 and β = 5 2 . Substitute α = − 5 2 and β = 5 2 in d 2 y d t 2 + ( α − 1 ) d y d t + β y = 0 . d 2 y d t 2 + ( − 5 2 − 1 ) d y d t + 5 2 y = 0 d 2 y d t 2 − 7 2 d y d t + 5 2 y = 0 y ″ − 7 2 y ′ + 5 2 y = 0 Obtain the characteristic equation by replacing y ″ with r 2 , y ′ with r and y with 1 in the differential equation: r 2 − 7 2 r + 5 2 = 0 . The roots of the characteristic equation are as follows. r 2 − 7 2 r + 5 2 = 0 r 1 , 2 = − ( − 7 2 ) ± ( − 7 2 ) 2 − 4 ( 1 ) ( 5 2 ) 2 ( 1 ) ( ∵ x 1 , 2 = − b

10th Edition

ISBN: 9780470458327

Author: William E. Boyce, Richard C. DiPrima

Publisher: Wiley, John & Sons, Incorporated

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 3.4, Problem 42P

To determine

The solution of the given differential equation using the substitution introduced problem 34 in Section 3.3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.4, Problem 41P

Chapter 3.4, Problem 43P

Students have asked these similar questions

1. Prove that for each n in N, 1+2++ n = n(n+1)/2. 2. Prove that for each n in N, 13 +23+ 3. Prove that for each n in N, 1+3+5+1 4. Prove that for each n ≥ 4,2" -1, then (1+x)" ≥1+nx for each n in N. 11. Prove DeMoivre's Theorem: fort a real number, (cost+i sint)" = cos nt + i sinnt for each n in N, where i = √√-1.

Pls help ASAP

2. Sam and Deb have a weekly net income of $1500. They have a pet dog. Their monthly expenses, not related to housing, are $2875. They have savings of $32 000. They are considering two housing options: Option 1: Renting a 2-bedroom condo for $1650 a month, plus utilities averaging $210 a month Option 2: Buying a 2-bedroom condo for a down payment of $24 500, bi-weekly mortgage payments of $1100, and a monthly condo fee of $475 a) Determine the monthly cost of each housing option. Factoring in other expenses not related to housing, which one can Sam and Deb afford? b) Suppose their dog falls ill and they have to pay $85 every week to cover veterinarian and medical expenses. Calculate the additional monthly expenses. How much money would be available for savings if they choose housing option 2?

Chapter 3 Solutions

Elementary Differential Equations

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.