Explanation Given: The differential function y 1 − x 2 y ' − x 1 − y 2 = 0 for y ( 0 ) = 1 . Formula used: ∫ x n d x = x n + 1 n + 1 , n ≠ − 1 Calculation: For the given function, y 1 − x 2 y ' − x 1 − y 2 = 0 for y ( 0 ) = 1 , the variables are separated calculated as follow, y 1 − x 2 y ' − x 1 − y 2 = 0 y 1 − x 2 d y = x 1 − y 2 d x y 1 − y 2 d y = x 1 − x 2 d x Now, integrate normally for, y and x , y 1 − y 2 d y = x 1 − x 2 d x Let, 1 − y 2 = u ⇒ − 2 y d y = d u Similarly, 1 − x 2 </

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ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 6.3, Problem 24E

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To calculate: The particular solution of the differential function using separation of variables satisfying the initial condition, y1−x2y'−x1−y2=0 for y(0)=1.

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The particular solution of the differential function using separation of variables satisfying the initial condition, y 1 − x 2 y ' − x 1 − y 2 = 0 for y ( 0 ) = 1 .

Solution Summary: The author explains how to calculate the differential function using separation of variables satisfying the initial condition.

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To calculate: The particular solution of the differential function using separation of variables satisfying the initial condition, y1−x2y'−x1−y2=0 for y(0)=1.

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