1. Consider the nonhomogeneous second order ODE y" + 4y = 10 sin(9 π t). (i) Beginning with the homogeneous version of ODE, find the characteristic equation by letting y = ext. (ii) Solve the characteristic equation then give the general solution to the homogeneous ODE. You do not have to derive the full solution - simply choose a standard form based on the solution to the characteristic equation. Let this solution be the complementary solution, yc. (iii) Let yp be the particular solution to the nonhomogeneous ODE. Choose a suitable trial solution, of similar form to 10 sin(9 π t), then solve for the unknown coefficients. ㅠ (iv) Give the full general solution y = yc + Yp. (v) Find the unique solution given the initial conditions y(0) = 6 and y'(0) = 4.
1. Consider the nonhomogeneous second order ODE y" + 4y = 10 sin(9 π t). (i) Beginning with the homogeneous version of ODE, find the characteristic equation by letting y = ext. (ii) Solve the characteristic equation then give the general solution to the homogeneous ODE. You do not have to derive the full solution - simply choose a standard form based on the solution to the characteristic equation. Let this solution be the complementary solution, yc. (iii) Let yp be the particular solution to the nonhomogeneous ODE. Choose a suitable trial solution, of similar form to 10 sin(9 π t), then solve for the unknown coefficients. ㅠ (iv) Give the full general solution y = yc + Yp. (v) Find the unique solution given the initial conditions y(0) = 6 and y'(0) = 4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:1. Consider the nonhomogeneous second order ODE y" + 4y = 10 sin(9 π t).
(i) Beginning with the homogeneous version of ODE, find the characteristic equation by letting
y=e¹t
(ii) Solve the characteristic equation then give the general solution to the homogeneous ODE. You
do not have to derive the full solution - simply choose a standard form based on the solution to
the characteristic equation. Let this solution be the complementary solution, yc.
(iii) Let yp be the particular solution to the nonhomogeneous ODE. Choose a suitable trial solution,
of similar form to 10 sin(9 π t), then solve for the unknown coefficients.
(iv) Give the full general solution y = ye + yp.
(v) Find the unique solution given the initial conditions y(0) = 6 and y'(0)
= 4.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
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
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,
