Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please help me with the interval portion. Thank you
![**Consider the following differential equations.**
\[ y \frac{dx}{dy} - x = 4y^2, \quad x(7) = 1 \]
**Find the coefficient function \(P(y)\) when the given differential equation is written in the standard form \(\frac{dx}{dy} + P(y)x = f(y)\).**
\[ P(y) = -\frac{1}{y} \]
**Find the integrating factor for the differential equation.**
\[ e^{\int P(y) \, dy} = \frac{1}{y} \]
**Solve the given initial-value problem.**
\[ x(y) = 4y^2 - \frac{195}{7}y \]
**Give the largest interval \(I\) over which the solution is defined. (Enter your answer using interval notation.)**
\[ I = (-\infty, 0) \cup (0, \infty) \] (This answer is indicated as incorrect.)](https://content.bartleby.com/qna-images/question/6589b73f-c70a-44b7-9b99-e4dd330855a5/f71374b2-dd32-4483-b02d-804c033c4969/gnlx09g_processed.png)
Transcribed Image Text:**Consider the following differential equations.**
\[ y \frac{dx}{dy} - x = 4y^2, \quad x(7) = 1 \]
**Find the coefficient function \(P(y)\) when the given differential equation is written in the standard form \(\frac{dx}{dy} + P(y)x = f(y)\).**
\[ P(y) = -\frac{1}{y} \]
**Find the integrating factor for the differential equation.**
\[ e^{\int P(y) \, dy} = \frac{1}{y} \]
**Solve the given initial-value problem.**
\[ x(y) = 4y^2 - \frac{195}{7}y \]
**Give the largest interval \(I\) over which the solution is defined. (Enter your answer using interval notation.)**
\[ I = (-\infty, 0) \cup (0, \infty) \] (This answer is indicated as incorrect.)
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