Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
[19] Consider (*) y" + 4y + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).

[19] Consider (*) y" + 4y + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).

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

My particular form solution looks like At^2+Bt+C+Dsin(4t)+Ecos(4t)+Fe^(2t), I know this is correct.

I keep getting sin(4t)*(-16D-16E+4D)+cos(4t)*9-16E+16D+4E) which reduces to sin(4t)*(-12D-16E)+cos(4t)*9-12E+16D) which gets me D=(-4/3)E and E=-47/18 which is wrong, I even plugged it into an online diffeq solver which shows D=2/5 and E=-3/10 respectively. So I know there's something wrong with my application of method of undetermined coefficients.

Enter an equation (and, optionally, the initial conditions): y"+4y'+4y=8t^2+10cos(4t)+8e^(2t) For example, y"(x)+25y(x)=0, y(0)=1, y'(0)=2. dy dx d²y Write y' (2) instead of y" (x) instead of etc. dx² If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below. CALCULATE Your input: solve 4y(t) + 4y' (t) + y″ (t) = 8t² + 8e²t + 10 cos (4t) ANSWER 2 sin (4t) 5 e2t y(t) = 2t²4t+ (C₁ + С₂t) e¯ + + 2 3 cos (4t) 10 +3
Transcribed Image Text:Enter an equation (and, optionally, the initial conditions): y"+4y'+4y=8t^2+10cos(4t)+8e^(2t) For example, y"(x)+25y(x)=0, y(0)=1, y'(0)=2. dy dx d²y Write y' (2) instead of y" (x) instead of etc. dx² If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below. CALCULATE Your input: solve 4y(t) + 4y' (t) + y″ (t) = 8t² + 8e²t + 10 cos (4t) ANSWER 2 sin (4t) 5 e2t y(t) = 2t²4t+ (C₁ + С₂t) e¯ + + 2 3 cos (4t) 10 +3
[19] Consider (*) y" +4y' + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).
Transcribed Image Text:[19] Consider (*) y" +4y' + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).
Expert 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