Consider x²y" - 12xy' + 42y = 0. Find all values of r such that y = x" satisfies the differen equation for x > 0. Enter as a comma separated list: help (numbers) Enter two linearly independent solutions of the form al help (formulas) r = 6, 7 Y1
Consider x²y" - 12xy' + 42y = 0. Find all values of r such that y = x" satisfies the differen equation for x > 0. Enter as a comma separated list: help (numbers) Enter two linearly independent solutions of the form al help (formulas) r = 6, 7 Y1
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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2.1.6. Ordinary
![Consider the differential equation:
\[ x^2y'' - 12xy' + 42y = 0. \]
Find all values of \( r \) such that \( y = x^r \) satisfies the differential equation for \( x > 0 \). Enter as a comma-separated list:
\[ r = 6, 7 \]
Enter two linearly independent solutions of the form above:
\[ y_1 = x^6 \]
\[ y_2 = x^7 \]
Now find a solution satisfying the initial values \( y(1) = 2, \quad y'(1) = 3 \):
\[ y = 25x^6 - 23x^7 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2Fb8303928-952f-45bd-9895-5476f562529d%2F5t9a90q_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the differential equation:
\[ x^2y'' - 12xy' + 42y = 0. \]
Find all values of \( r \) such that \( y = x^r \) satisfies the differential equation for \( x > 0 \). Enter as a comma-separated list:
\[ r = 6, 7 \]
Enter two linearly independent solutions of the form above:
\[ y_1 = x^6 \]
\[ y_2 = x^7 \]
Now find a solution satisfying the initial values \( y(1) = 2, \quad y'(1) = 3 \):
\[ y = 25x^6 - 23x^7 \]
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