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