Consider the following initial-value problem. Let af = (x + y)² = x² + 2xy + y². Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ?х f(x, y) = (x + y)² dx + (2xy + x² - 3) dy = 0, y(1) = 1 h'(y) = + h(y) Find the derivative of h(y). Solve the given initial-value problem.
Consider the following initial-value problem. Let af = (x + y)² = x² + 2xy + y². Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. ?х f(x, y) = (x + y)² dx + (2xy + x² - 3) dy = 0, y(1) = 1 h'(y) = + h(y) Find the derivative of h(y). Solve the given initial-value problem.
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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![Consider the following initial-value problem.
Let
af
= (x + y)² = x² + 2xy + y². Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y.
?х
f(x, y) =
(x + y)² dx + (2xy + x² - 3) dy = 0, y(1) = 1
h'(y) =
+ h(y)
Find the derivative of h(y).
Solve the given initial-value problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0143c836-8f2c-4043-b7b3-58e093f2fd4b%2F174545bd-5415-4e14-b4dc-86cbcf44c2b4%2Ff3r82qm_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following initial-value problem.
Let
af
= (x + y)² = x² + 2xy + y². Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y.
?х
f(x, y) =
(x + y)² dx + (2xy + x² - 3) dy = 0, y(1) = 1
h'(y) =
+ h(y)
Find the derivative of h(y).
Solve the given initial-value problem.
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