8. yiv5y" + 4y = 10e y" (0) = 0, y"" (0) = 0 9. yiv = 1 y + 5y" + 4y = 90 sin 4x, y(0) = y" (0) = -1, y" (0) = -32 10. x³y" + xy' - y = x², y(1) = 1, y' (1 y" (1) = 14 -3x y(0) = 1,
8. yiv5y" + 4y = 10e y" (0) = 0, y"" (0) = 0 9. yiv = 1 y + 5y" + 4y = 90 sin 4x, y(0) = y" (0) = -1, y" (0) = -32 10. x³y" + xy' - y = x², y(1) = 1, y' (1 y" (1) = 14 -3x y(0) = 1,
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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Question
please help with problem 10 follow provided instructions
please do not provide solution in image format thank you!
![### Differential Equations Problems
#### Problem 8
\[ y^{(4)} - 5y'' + 4y = 10e^{-3x} \]
**Initial Conditions:**
- \( y(0) = 1 \)
- \( y'(0) = 0 \)
- \( y''(0) = 0 \)
- \( y'''(0) = 0 \)
#### Problem 9
\[ y^{(4)} + 5y'' + 4y = 90 \sin 4x \]
**Initial Conditions:**
- \( y(0) = 1 \)
- \( y'(0) = 2 \)
- \( y''(0) = -1 \)
- \( y'''(0) = -32 \)
#### Problem 10
\[ x^3y''' + xy' - y = x^2 \]
**Initial Conditions:**
- \( y(1) = 1 \)
- \( y'(1) = 3 \)
- \( y''(1) = 14 \)
These problems involve higher-order differential equations, each with given initial conditions specified at \( x = 0 \) or \( x = 1 \). The solutions to such equations often require methods such as characteristic equations, undetermined coefficients, variation of parameters, or employing Laplace transforms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7f7e91-311f-40b2-8ef2-058480eb16a0%2F8533a6bb-4c64-4b81-a34a-6c4c9298a5a6%2Fbu7w63g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Differential Equations Problems
#### Problem 8
\[ y^{(4)} - 5y'' + 4y = 10e^{-3x} \]
**Initial Conditions:**
- \( y(0) = 1 \)
- \( y'(0) = 0 \)
- \( y''(0) = 0 \)
- \( y'''(0) = 0 \)
#### Problem 9
\[ y^{(4)} + 5y'' + 4y = 90 \sin 4x \]
**Initial Conditions:**
- \( y(0) = 1 \)
- \( y'(0) = 2 \)
- \( y''(0) = -1 \)
- \( y'''(0) = -32 \)
#### Problem 10
\[ x^3y''' + xy' - y = x^2 \]
**Initial Conditions:**
- \( y(1) = 1 \)
- \( y'(1) = 3 \)
- \( y''(1) = 14 \)
These problems involve higher-order differential equations, each with given initial conditions specified at \( x = 0 \) or \( x = 1 \). The solutions to such equations often require methods such as characteristic equations, undetermined coefficients, variation of parameters, or employing Laplace transforms.
Transcribed Image Text:### Higher-Order Ordinary Differential Equations (ODEs)
**Objective:** Find the final solutions of the 3rd-order linear nonhomogeneous ODEs in **Problems 1, 2, and 10**.
- **Problem 1:** Utilize both the Method of Undetermined Coefficients (MUC) and the Variation of Parameters (VOP).
- **Problem 2:** Utilize the Method of Undetermined Coefficients (MUC) only.
- **Problem 10:** Utilize the Variation of Parameters (VOP) only.
By applying these methods, you'll get a comprehensive understanding of the techniques used to solve higher-order linear nonhomogeneous ODEs.
For more details on these methods, check the respective sections on the **Method of Undetermined Coefficients** and **Variation of Parameters**.
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