eginning with the homogeneous version of ODE, find the characteristic e = ext. olve the characteristic equation then give the general solution to the homog o not have to derive the full solution - simply choose a standard form based e characteristic equation. Let this solution be the complementary solution, ? et y be the particular solution to the nonhomogeneous ODE. Choose a suit similar form to 10 sin(97t), then solve for the unknown coefficients. ive the full general solution y = Yc+Yp. nd the unique solution given the initial conditions y(0) = 6 and y'(0) = 4.
eginning with the homogeneous version of ODE, find the characteristic e = ext. olve the characteristic equation then give the general solution to the homog o not have to derive the full solution - simply choose a standard form based e characteristic equation. Let this solution be the complementary solution, ? et y be the particular solution to the nonhomogeneous ODE. Choose a suit similar form to 10 sin(97t), then solve for the unknown coefficients. ive the full general solution y = Yc+Yp. nd 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
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Question
Please show solution to each step of the problem. (i, ii, iii, iv and v)
Transcribed Image Text:1. Consider the nonhomogeneous second order ODE y" + 4y = 10 sin(9 í 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 = y + yp.
(v) Find the unique solution given the initial conditions y(0) = 6 and y'(0)
= 4.
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