Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(1) First verify that yn and 2 are solutions of the following differential equations, then find a particular solution of the form y=ch+2 that satisfies the given initial conditions. Primes denote derivatives with respect to z. (a) y-y=0; -, /2; y(0)-0, y'(0)-5. (b) z²" +2ry-6y=0; -², 2-³; (2)-10, (2) - 15.

(1) First verify that yn and 2 are solutions of the following differential equations, then find a particular solution of the form y=ch+2 that satisfies the given initial conditions. Primes denote derivatives with respect to z. (a) y-y=0; -, /2; y(0)-0, y'(0)-5. (b) z²" +2ry-6y=0; -², 2-³; (2)-10, (2) - 15.

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%

HW6P1

 

(1) First verify that y₁ and 2 are solutions of the following differential equations, then find a particular solution of the form y = ₁3/1+022 that satisfies the given initial conditions. Primes denote derivatives with respect to z. (a) y - y = 0; h=², 1/₂=²; y(0) = 0, y/'(0) = 5. (b) x²y" + 2xy-6y=0; ₁=², 1/₂ = ³; (2) = 10, (2) = 15. (2) Show that 1/1 = ² and 2 = ³ are two solutions of zy" - Ary' +6y= 0, both satisfying the initial conditions y(0) = 0 ='(0). Explain why these facts do not contradict Theorem 2 (with respect to the guaranteed uniqueness). (3) Find the general solutions of the differential equation: Ay" - 12y +9y=0. (4) Solve the initial value problem: (5) Solve the initial value problem: "-6y +25y=0; y(0) = 3, y(0) = 1. "+"=0; y(0) = -1, (0) = 0, "(0) = 1.
Transcribed Image Text:(1) First verify that y₁ and 2 are solutions of the following differential equations, then find a particular solution of the form y = ₁3/1+022 that satisfies the given initial conditions. Primes denote derivatives with respect to z. (a) y - y = 0; h=², 1/₂=²; y(0) = 0, y/'(0) = 5. (b) x²y" + 2xy-6y=0; ₁=², 1/₂ = ³; (2) = 10, (2) = 15. (2) Show that 1/1 = ² and 2 = ³ are two solutions of zy" - Ary' +6y= 0, both satisfying the initial conditions y(0) = 0 ='(0). Explain why these facts do not contradict Theorem 2 (with respect to the guaranteed uniqueness). (3) Find the general solutions of the differential equation: Ay" - 12y +9y=0. (4) Solve the initial value problem: (5) Solve the initial value problem: "-6y +25y=0; y(0) = 3, y(0) = 1. "+"=0; y(0) = -1, (0) = 0, "(0) = 1.
Expert Solution
Step 1

Note: " As per our guidelines we will solve the first question . If you want any specific question to be solved please specify that question or post only that question . " 

(1)

(a).   y''-y=0    ;    y1=ex  ,  y2=e-x              ;  y(0)=0  ,   y'(0) = 5

(b).                                                                         x2y''+2xy-6y=0  ;  y1= x2 , y2= x-3         ;  y(2)=10  ,  y'(2) = 15

(.) If  y1 ,  y2 are the solution of a differential equation then  y1 , y2 satisfy the differential equation .

steps

Step by step

Solved in 7 steps

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