Consider the ODE y''-4y'+5y=0, which satisfied by the homoegenous solution yH=c1e2tcos(t)+c2te2tsin(t). Determine the form of the particaular solution for the DEs below. DO NOT EVALUATE THE COEFFICIENTS. 1. y''-4y+5y=2t2e2t 2. y''-4y'+5y=9tcos(t)

Consider the ODE y''-4y'+5y=0, which satisfied by the homoegenous solution yH=c1e2tcos(t)+c2te2tsin(t). Determine the form of the particaular solution for the DEs below. DO NOT EVALUATE THE COEFFICIENTS. 1. y''-4y+5y=2t2e2t 2. y''-4y'+5y=9tcos(t)

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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Differential Equations

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Question

Consider the ODE y''-4y'+5y=0, which satisfied by the homoegenous solution y_H=c₁e^2tcos(t)+c₂te^2tsin(t). Determine the form of the particaular solution for the DEs below. DO NOT EVALUATE THE COEFFICIENTS.

1. y''-4y+5y=2t²e^2t

2. y''-4y'+5y=9tcos(t)

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