Q5. Find the general solution to the following set of ODES. y₁ = y₁ + y2 + sint y₂ = 4y1 + y2
Q5. Find the general solution to the following set of ODES. y₁ = y₁ + y2 + sint y₂ = 4y1 + y2
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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![**Q5.** Find the general solution to the following set of ODEs.
\[
y_1' = y_1 + y_2 + \sin t
\]
\[
y_2' = 4y_1 + y_2
\]
This is a system of linear ordinary differential equations involving two functions, \(y_1\) and \(y_2\), along with their derivatives. The equations are coupled, meaning each equation involves both functions. The task is to find the general solutions for \(y_1\) and \(y_2\) with respect to \(t\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09f7f533-d4af-4401-a50a-ccb3ef26e16d%2F589b9f32-faf8-44dc-8a10-356dd3af4ad9%2Fnlco9j5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Q5.** Find the general solution to the following set of ODEs.
\[
y_1' = y_1 + y_2 + \sin t
\]
\[
y_2' = 4y_1 + y_2
\]
This is a system of linear ordinary differential equations involving two functions, \(y_1\) and \(y_2\), along with their derivatives. The equations are coupled, meaning each equation involves both functions. The task is to find the general solutions for \(y_1\) and \(y_2\) with respect to \(t\).
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Step 1: Description
Here we firstly, find the value of y1 and then by putting the value of y1 in equation (i) we find value of y2.
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