Consider the following differential equations. x = 4y², x(7) = 1 P(y) = dx Find the coefficient function P(y) when the given differential equation is written in the standard form + P(y)x = f(y). dy у e/P(y)dy = = dx dy 1 y Find the integrating factor for the differential equation. 1 y Solve the given initial-value problem. x(y) = 4y²- 195 y 7 Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.) 1 = (-∞,0) U (0,0)
Consider the following differential equations. x = 4y², x(7) = 1 P(y) = dx Find the coefficient function P(y) when the given differential equation is written in the standard form + P(y)x = f(y). dy у e/P(y)dy = = dx dy 1 y Find the integrating factor for the differential equation. 1 y Solve the given initial-value problem. x(y) = 4y²- 195 y 7 Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.) 1 = (-∞,0) U (0,0)
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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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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6589b73f-c70a-44b7-9b99-e4dd330855a5%2Ff71374b2-dd32-4483-b02d-804c033c4969%2Fgnlx09g_processed.png&w=3840&q=75)
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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