From the following differential equation Check that the yi are solutions, determine if they are linearly independent, construct a linear equation and verify that it satisfies the edo, calculate the value of the integration constants y" - 3y"+y' - 3y = 0 Y₁ = e³x y₂ = sin(x) y(0) = 3 y'(0) = −1 Y3 = cos(x) y"(0) = -2
From the following differential equation Check that the yi are solutions, determine if they are linearly independent, construct a linear equation and verify that it satisfies the edo, calculate the value of the integration constants y" - 3y"+y' - 3y = 0 Y₁ = e³x y₂ = sin(x) y(0) = 3 y'(0) = −1 Y3 = cos(x) y"(0) = -2
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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![From the following differential equation
Check that the yi are solutions, determine if they are linearly independent,
construct a linear equation and verify that it satisfies the edo, calculate the value
of the integration constants
y"
- 3y"+y' - 3y = 0
y₁ = e³x
y₂ = sin(x)
y(0) = 3 y'(0) = −1
Y3 = cos(x)
y"(0) = -2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e4fdfb9-3c00-4b1f-b4f4-b7cd4fa3e045%2F0f319b0d-0fe2-461f-844c-b0ca5d42bbd5%2F1unxwd0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:From the following differential equation
Check that the yi are solutions, determine if they are linearly independent,
construct a linear equation and verify that it satisfies the edo, calculate the value
of the integration constants
y"
- 3y"+y' - 3y = 0
y₁ = e³x
y₂ = sin(x)
y(0) = 3 y'(0) = −1
Y3 = cos(x)
y"(0) = -2
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Step 1: Write some theorems corresponding to a nth order homogeneous linear differential equation
VIEWStep 2: Verify that the given three functions are solutions of the given equation
VIEWStep 3: Proved that the three solutions are Linearly independent solutions of the given equation
VIEWStep 4: Construct a linear equation that satisfies the given equation
VIEWStep 5: Determine the value of the constant of integration
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