Find the general solution to y" - 6y +9y 5 y(x) = y(x) + C₁y₁ (x) + C₂y2(x) with y₂ = x5 Y₁ = and Y2 = e³x Choose all terms as simple as possible. The order of y₁ and y2 does not matter. Note that, unlike the previous one, this problem requires variation of parameters.
Find the general solution to y" - 6y +9y 5 y(x) = y(x) + C₁y₁ (x) + C₂y2(x) with y₂ = x5 Y₁ = and Y2 = e³x Choose all terms as simple as possible. The order of y₁ and y2 does not matter. Note that, unlike the previous one, this problem requires variation of parameters.
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 4 (not yet completed)**
Find the general solution to \( y'' - 6y' + 9y = \frac{5}{x^5} e^{3x} \).
\[ y(x) = y_p(x) + C_1 y_1(x) + C_2 y_2(x) \text{ with } y_p = \]
\[ y_1 = \] (blank) \quad and \quad \( y_2 = \) (blank)
Choose all terms as simple as possible. The order of \( y_1 \) and \( y_2 \) does not matter.
Note that, unlike the previous one, this problem requires variation of parameters.
**Submit** (button)
_Last change: 2022/10/25_](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67b47c5-7500-437e-a792-0397277503d2%2F4bcd12e0-4ee5-4fa9-80d1-c8ea43219ecc%2Fumnfhc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4 (not yet completed)**
Find the general solution to \( y'' - 6y' + 9y = \frac{5}{x^5} e^{3x} \).
\[ y(x) = y_p(x) + C_1 y_1(x) + C_2 y_2(x) \text{ with } y_p = \]
\[ y_1 = \] (blank) \quad and \quad \( y_2 = \) (blank)
Choose all terms as simple as possible. The order of \( y_1 \) and \( y_2 \) does not matter.
Note that, unlike the previous one, this problem requires variation of parameters.
**Submit** (button)
_Last change: 2022/10/25_
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