Solution Found!
Given that is a solution to And is a solution to use the
Chapter 4, Problem 2E(choose chapter or problem)
Given that \(y_{1}(t)=\cos t\) is a solution to
\(y^{\prime \prime}-y^{\prime}+y=\sin t\)
and \(y^{\prime \prime}-y^{\prime}+y=\sin t\) is a solution to \(y^{\prime \prime}-y^{\prime}+y=e^{2}\),
use the superposition principle to find solutions to the following differential equations:
(a) \(y^{\prime \prime}-y^{\prime}+y=5 \sin t\).
(b) \(y^{\prime \prime}-y^{\prime}+y=\sin t-3 e^{2 t}\).
(c) \(y^{\prime \prime}-y^{\prime}+y=4 \sin t+18 e^{2 t}\).
Equation Transcription:
Text Transcription:
y_1(t)=cos t
y''-y'+y=sin t
y_2(t)=e^2t /3
y''-y'+y=e^2t
y''-y'+y=5 sin t
y''-y'+y=sin t-3e^2t
y''-y'+y=4 sin t+18e^2t
Questions & Answers
QUESTION:
Given that \(y_{1}(t)=\cos t\) is a solution to
\(y^{\prime \prime}-y^{\prime}+y=\sin t\)
and \(y^{\prime \prime}-y^{\prime}+y=\sin t\) is a solution to \(y^{\prime \prime}-y^{\prime}+y=e^{2}\),
use the superposition principle to find solutions to the following differential equations:
(a) \(y^{\prime \prime}-y^{\prime}+y=5 \sin t\).
(b) \(y^{\prime \prime}-y^{\prime}+y=\sin t-3 e^{2 t}\).
(c) \(y^{\prime \prime}-y^{\prime}+y=4 \sin t+18 e^{2 t}\).
Equation Transcription:
Text Transcription:
y_1(t)=cos t
y''-y'+y=sin t
y_2(t)=e^2t /3
y''-y'+y=e^2t
y''-y'+y=5 sin t
y''-y'+y=sin t-3e^2t
y''-y'+y=4 sin t+18e^2t
ANSWER:
Solution:
Step 1:
In this problem, we need to find the solution for the given following conditions by superposition principle.