Consider the DE: dr – e* dy = 0. (a) For what values of a and B is this DE a homogeneous DE? (b) Use the values a, B you suggested in (a) and find the solution that satisfies the initial condition y(1) = 0.
Consider the DE: dr – e* dy = 0. (a) For what values of a and B is this DE a homogeneous DE? (b) Use the values a, B you suggested in (a) and find the solution that satisfies the initial condition y(1) = 0.
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:
**2. Consider the DE:**
\[ \left[ 1 + \left( \frac{y^\beta}{x} \right) e^{\frac{y}{x}} \right] dx - e^{\frac{y}{x}} dy = 0. \]
**Tasks:**
(a) For what values of \(\alpha\) and \(\beta\) is this DE a homogeneous DE? [2 points]
(b) Use the values \(\alpha\), \(\beta\) you suggested in (a) and find the solution that satisfies the initial condition \(y(1) = 0\). [6 points]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4e4c829-f598-4523-ba66-76332cdb1366%2F10f99933-e9d7-4402-af79-399bd9b273cc%2Fuz6j8p9_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**2. Consider the DE:**
\[ \left[ 1 + \left( \frac{y^\beta}{x} \right) e^{\frac{y}{x}} \right] dx - e^{\frac{y}{x}} dy = 0. \]
**Tasks:**
(a) For what values of \(\alpha\) and \(\beta\) is this DE a homogeneous DE? [2 points]
(b) Use the values \(\alpha\), \(\beta\) you suggested in (a) and find the solution that satisfies the initial condition \(y(1) = 0\). [6 points]
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