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2 ½ Solve (2+ 2x y")y dr + (x*y" + 2)x dy = 0. %3D

2 ½ Solve (2+ 2x y")y dr + (x*y" + 2)x dy = 0. %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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just how it did derived to the finalanswer. SHOW COMPLETE SOLUTIONS

J 20. solve (2+ 2x*y"y dx - 2)x dy = + (x y + : 0. 2v 4v dx reduces the equation x' The suggested transformation x*y = v, y to 2v (2 + 2v)– dx + x (v + 2) (= dv 2 4v dx) = 0 or v(3+ v)dx - x(v + 2)dv : 0. 4 dx Then 1 dv : 0. 3 v + 3 2 dv 3 In x - 2 In v - In (v + 3) = In C4, } = C,u° (u + 3), %3D 3 v 2 ½ and C,zy(x'y"+ 3) xy(x y"+ 3) = C. 1 = or %3D
Transcribed Image Text:J 20. solve (2+ 2x*y"y dx - 2)x dy = + (x y + : 0. 2v 4v dx reduces the equation x' The suggested transformation x*y = v, y to 2v (2 + 2v)– dx + x (v + 2) (= dv 2 4v dx) = 0 or v(3+ v)dx - x(v + 2)dv : 0. 4 dx Then 1 dv : 0. 3 v + 3 2 dv 3 In x - 2 In v - In (v + 3) = In C4, } = C,u° (u + 3), %3D 3 v 2 ½ and C,zy(x'y"+ 3) xy(x y"+ 3) = C. 1 = or %3D
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