Solution Found!
Given that is a solution to and that is a solution to ,
Chapter 4, Problem 1E(choose chapter or problem)
Given that \(y_{1}(t)=(1 / 4) \sin 2 t\) is a solution to \(y^{\prime \prime}+2 y^{\prime}+4 y=\cos 2 t\) and that \(y_{2}(t)=t / 4-1 / 8\) is a solution to \(y^{\prime \prime+2 y+4 y=\), use the superposition principle to find solutions to the following:
(a) \(y^{\prime \prime}+2 y^{\prime}+4 y=t+\cos 2 t\).
(b) ‘(y^{\prime \prime}+2 y+4 y=2 t-3 \cos 2 t\.
(c) \(y^{\prime \prime}+2 y^{\prime}+4 y=11 t-12 \cos 2 t\).
Equation Transcription:
Text Transcription:
y_1(t)=(1/4)sin 2t
y''+2y'+4y=cos 2t
y_2(t)=t/4-1/8
y''+2y'+4y=t
y''+2y'+4y=t+cos 2t
y''+2y'+4y=2t-3 cos 2t
y''+2y'+4y=11t-12 cos 2t
Questions & Answers
QUESTION:
Given that \(y_{1}(t)=(1 / 4) \sin 2 t\) is a solution to \(y^{\prime \prime}+2 y^{\prime}+4 y=\cos 2 t\) and that \(y_{2}(t)=t / 4-1 / 8\) is a solution to \(y^{\prime \prime+2 y+4 y=\), use the superposition principle to find solutions to the following:
(a) \(y^{\prime \prime}+2 y^{\prime}+4 y=t+\cos 2 t\).
(b) ‘(y^{\prime \prime}+2 y+4 y=2 t-3 \cos 2 t\.
(c) \(y^{\prime \prime}+2 y^{\prime}+4 y=11 t-12 \cos 2 t\).
Equation Transcription:
Text Transcription:
y_1(t)=(1/4)sin 2t
y''+2y'+4y=cos 2t
y_2(t)=t/4-1/8
y''+2y'+4y=t
y''+2y'+4y=t+cos 2t
y''+2y'+4y=2t-3 cos 2t
y''+2y'+4y=11t-12 cos 2t
ANSWER:
Solution:
Step 1:
In this problem, we need to find the solution for the given following conditions by superposition principle.