х+2 у-1) dx- (2х+4 у-3) dy%3D0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 28E
Related questions
Question
Find the General/ Particular Solution of the Given differential Equation.
- for the 2nd picture
For the 1st picture, it is just an example on how to solve the equation, you must state what kind of process did you use.
Transcribed Image Text:(х+2у-1) dx -(2x+4 у-3)dy3D0
Transcribed Image Text:1.
(х-3у) dy+(x+2у) dx%3D0
Solution: Homogeneous
(x-3 y)dy+(x+2 y) dx=0
> Homogeneous equations
let v=X
y
Substitution
x=vy
dx=vdy+y dv
Solving for dx, substitution
Solve Problems
dy (v+2)
> Separation of Variables
·dv=0
y '(v²+3v-3)
(v+2)
(v²+3v-3)
> Integration
了业+
dv=C
y
> Integration by substitution
u=v+3v-3
1 S(2 v+3)
ay*\v+3v-3)
2 (v²+3v-3)
(v²+3v-3)
> Techniques like integration
of partial fraction can also
be used in solving this
problem
In y+ In (v²+3v-3)+ f dv
=C
3
V+.
2 In y +In (v²+3v-3)+ [ dv
=2C
> Integration by completing a
V+
square
let 2C=C,
> a constant is just another
V
constant
In y’ +In (v² +3v-3)+(G n-
-)=C,
3
V+2
Integration
fraction
by
Another
partial
or
(v-2
y*(v*+3v-3) -
(v+을)
y'(v*+3v-3}(v=A(v+
-= 2e, ,let 2 e =A
S du
u-a
-In
2
2
u -a
3
2
u+a
> Simplifying the Equation
V-:
3
3
> Substitution
to
original
2
function x and y
y
у
(x*+3xy-3 y*) (2x–3 y),
)=A
2 у
(2 x+3 y)
General Solution
y
'2 y
v(x*+3 xy-3 y*) (2x-3 y),
2у
(x²+3 xy-3 y')*(2x-3 y)=Ay°(2x+3 y)
y
)=A2x+3y)
'2 y
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