(х+2у -1) dx - (2x+4 у-3) dy%3D0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:3.
(x-2 y+2)dx+(3x-6y-1)dy=0
Solution:
> Evaluation of type of Equation
(x-2y+2)dx+(3x-6y-1)dy=0
let z=x-2 y
dz=dx-2 dy
(z+2)(dz+2dy)+(3z-1)dy=0
(z+2)dz+(5 z+3)dy=0
(z+2)
(5z+3)
(5z+10) dz+5dy=0
(5z+3)
(5z+3+7)
(5z+3)
> Parallel Equations
%3D
|
> Separation of Variables
-dz+dy=0
> Integration of rational Fraction\
-dz +5 dy=0
> you can split also 10 into 3 and 7
to simplify the integration
dz
process
S dz+
-+5J dy=0
f 7
(5z+3)
> Integration
z+In(5z+3)+5 y=C
> General Solution
7
x-2 y+ In (5(x-2 y)+3)+5y=C
7
x+3 y+In(10x-10 y +3)=C
5
Transcribed Image Text:(х+2у-1) dx -(2x+4 у-3)dy3D0
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