To determine The solution of the given IVP and graph the solution. Explanation Given: The given IVP is y ′ ′ ′ + 3.2 y ″ + 4.81 y ′ = 0 , y ( 0 ) = 3.4 , y ′ ( 0 ) = − 4.6 , y ″ ( 0 ) = 9.91 . Procedure used: Let y ( n ) + a n − 1 ( x ) y ( n − 1 ) + ⋯ + a 1 ( x ) y ′ + a 0 ( x ) y = r ( x ) be the n th order homogeneous ODE with constant coefficients, where y ( n ) = d n y d x n is the first term and r ( x ) ≠ 0 . A general solution of the above equation on an open interval I of the x -axis is of the form r ( x ) ≠ 0 Obtain the characteristic equation by substituting y = e λ x in the ODE as follows. y ( x ) = y h ( x ) + y p ( x ) Here y h ( x ) is a general solution of the corresponding homogeneous ODE. And y p ( x ) is any solution of the given equation on I containing no arbitrary constants. Calculation: Consider the given IVP, y ′ ′ ′ + 3.2 y ″ + 4.81 y ′ = 0 , y ( 0 ) = 3.4 , y ′ ( 0 ) = − 4.6 , y ″ ( 0 ) = 9.91 Consider the homogeneous equation of the given ODE, y ′ ′ ′ + 3.2 y ″ + 4.81 y ′ = 0 Obtain the characteristic equation as follows. λ 3 + 3.2 λ 2 + 4.81 λ = 0 Compute the roots of the characteristic equation as follows. λ ( λ 2 + 3.2 λ + 4.81 ) = 0 λ 1 = 0 or λ = − 3.2 ± 3.2 2 − 4 ( 1 ) ( 4.81 ) 2 λ 1 = 0 or λ = − 3.2 ± 3 i 2 λ 1 = 0 or λ 2 = − 1.6 + 1.5 i or λ 3 = − 1.6 − 1.5 i The solution of the given ODE is given as follows. y = c 1 e 0 + c 2 e − 1.6 x cos ( 1.5 x ) + c 3 e − 1.6 x sin ( 1.5 x ) = c 1 + c 2 e − 1.6 x cos ( 1.5 x ) + c 3 e − 1.6 x sin ( 1.5 x ) Obtain the first 2 derivatives of the general solution obtained as follows. y = c 1 + c 2 e − 1.6 x cos ( 1.5 x ) + c 3 e − 1.6 x sin ( 1.5 x ) y ′ = − 1.6 c 2 e − 1.6 x cos ( 1.5 x ) − 1.5 c 2 e − 1.6 x sin ( 1.5 x ) − 1.6 c 3 e − 1.6 x sin ( 1.5 x ) + 1.5 c 3 e − 1.6 x cos ( 1.5 x ) = e − 1.6 x sin ( 1.5 x ) ( − 1.5 c 2 − 1.6 c 3 ) + e − 1.6 x cos ( 1.5 x ) ( 1.5 c 3 − 1.6 c 2 ) y ″ = [ ( − 1

10th Edition

ISBN: 9781119480150

Author: Kreyszig

Publisher: WILEY C

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 3.2, Problem 7P

To determine

The solution of the given IVP and graph the solution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.2, Problem 6P

Chapter 3.2, Problem 8P

Students have asked these similar questions

Determine the volume and the surface area of the shape obtained by rotating the area of the figure about the x-axis and the y-axis.

I'm getting only chatgpt answer that are wrong Plz don't use chatgpt answer will upvote .

Find xyz cordinates of center of gravity given z = 3.47 in

Chapter 3 Solutions

ADVANCED ENGINEERING MATH.>CUSTOM<

Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - 1–6 BASES: TYPICAL EXAMPLES To get a feel for...Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P Ch. 3.1 - Prob. 11P

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.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Basic Technical Mathematics
Advanced Math
ISBN:9780134437705
Author:Washington
Publisher:PEARSON
Topology
Advanced Math
ISBN:9780134689517
Author:Munkres, James R.
Publisher:Pearson,

Advanced Engineering Mathematics

Advanced Math

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:9780073397924

Author:Steven C. Chapra Dr., Raymond P. Canale

Publisher:McGraw-Hill Education

Introductory Mathematics for Engineering Applicat...

Advanced Math

ISBN:9781118141809

Author:Nathan Klingbeil

Publisher:WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:9781337798310

Author:Peterson, John.

Publisher:Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:9780134437705

Author:Washington

Publisher:PEARSON

Topology

Advanced Math

ISBN:9780134689517

Author:Munkres, James R.

Publisher:Pearson,

SEE MORE TEXTBOOKS

01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY

Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY

Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY