Ive the differential equation x - 2y) dx + (y In (y - x)² + (x b. In (y - x)² + (x 1) dy = 0 1) + 2 arctan − 4 arctan x)² + (x − 1)²|+2 arctan (2−7) − 1) c. In ln|(y − d. In (y - x)² + (x − 1)²| - + (2 − 1) – 4 arctan - y -x x+1 x-y x+1 = C = C = C (z-i) ( ² = 1 ) = C с

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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Using Homogenous Differential Equation

Solve the differential equation
(2x
a.
b.
2y) dx + (y − 1) dy = 0
ln|(y − x)² + (x − 1)²| + 2 arctan (1+1)
In (y − x)² + (x − 1)²|
4 arctan
-
x) + (2 − 1) +2 arctan
x)².
a\(y –
c. In
− 1) − 4 arctan
− x)² (x
-
d. In|(y – x) + (z
x- Y
x + 1
- I
x -
= C
=
= C
=
= C
x
(²³) =
1
= C
Transcribed Image Text:Solve the differential equation (2x a. b. 2y) dx + (y − 1) dy = 0 ln|(y − x)² + (x − 1)²| + 2 arctan (1+1) In (y − x)² + (x − 1)²| 4 arctan - x) + (2 − 1) +2 arctan x)². a\(y – c. In − 1) − 4 arctan − x)² (x - d. In|(y – x) + (z x- Y x + 1 - I x - = C = = C = = C x (²³) = 1 = C
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