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show how it did derived to the final answer.show complete solutions

show how it did derived to the final answer.show complete solutions

Advanced Engineering Mathematics
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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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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