Solve the differential equation by variation of parameters. y" + y = sin2(x) y(x) = %3D
Solve the differential equation by variation of parameters. y" + y = sin2(x) y(x) = %3D
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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![**Problem Statement:**
Solve the differential equation by variation of parameters.
\[ y'' + y = \sin^2(x) \]
**Solution:**
\[ y(x) = \boxed{} \]
**Explanation:**
This problem involves solving a non-homogeneous second-order differential equation using the method of variation of parameters. The given equation is:
\[ y'' + y = \sin^2(x) \]
The left side displays a linear combination of a second derivative and the function itself, while the right side is a trigonometric function squared. To solve it using variation of parameters, follow these general steps:
1. Solve the corresponding homogeneous equation: \( y'' + y = 0 \).
2. Find the particular solution using variation of parameters for the non-homogeneous equation.
3. Combine solutions from the homogeneous and particular solutions to get the general solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F711908d8-7456-4dad-baa5-347305ed075d%2Feed03c5a-06b2-4a5a-8040-094d812b2434%2F8t9krlt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the differential equation by variation of parameters.
\[ y'' + y = \sin^2(x) \]
**Solution:**
\[ y(x) = \boxed{} \]
**Explanation:**
This problem involves solving a non-homogeneous second-order differential equation using the method of variation of parameters. The given equation is:
\[ y'' + y = \sin^2(x) \]
The left side displays a linear combination of a second derivative and the function itself, while the right side is a trigonometric function squared. To solve it using variation of parameters, follow these general steps:
1. Solve the corresponding homogeneous equation: \( y'' + y = 0 \).
2. Find the particular solution using variation of parameters for the non-homogeneous equation.
3. Combine solutions from the homogeneous and particular solutions to get the general solution.
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