Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution. COS X X is a

6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution. COS X X is a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
4/5: Please solve the following differential equations marked with a red circle.
**Question 4:** In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. (a) \( y_1 = 2e^{3t} - 5e^{-t}, \quad y_2 = 11e^{-t} \) (b) \( y_1 = \cos(\pi t), \quad y_2 = \sin(\pi t) \) (c) \( y_1 = e^{2t} \cos(5t), \quad y_2 = e^{2t} \sin(5t) \) (d) \( y_1 = e^{3t}, \quad y_2 = te^{3t} \) **Question 5:** Find the general solution of the equation \( xy'' + 2y' + xy = 0 \), if we know that \( y_1 = \frac{\cos x}{x} \) is a solution.
Transcribed Image Text:**Question 4:** In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. (a) \( y_1 = 2e^{3t} - 5e^{-t}, \quad y_2 = 11e^{-t} \) (b) \( y_1 = \cos(\pi t), \quad y_2 = \sin(\pi t) \) (c) \( y_1 = e^{2t} \cos(5t), \quad y_2 = e^{2t} \sin(5t) \) (d) \( y_1 = e^{3t}, \quad y_2 = te^{3t} \) **Question 5:** Find the general solution of the equation \( xy'' + 2y' + xy = 0 \), if we know that \( y_1 = \frac{\cos x}{x} \) is a solution.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS