Classify the following differential equations as separable, homogeneous, parallel line,

obrozenecy6

obrozenecy6

Answered question

2021-12-31

Classify the following differential equations as separable, homogeneous, parallel line, or exact. Explain briefly your answers. Then, solve each equation according to their classification. (2x3y)dx+(2y3x)dy=0

Answer & Explanation

Archie Jones

Archie Jones

Beginner2022-01-01Added 34 answers

Classsify the following differential eq.
(2x3y)dx+(2y3x)dy=0
Solution:
dy(2y3x)=(2x3y)dx
dydx=(2x3y)(2y3x)
Finding homogeneous
F(λx,λy)=(2λx3λy)(2λy3λx)
=λ(2x3y)(2y3x)
=(2x3y)(2x3x)
=λF(r,y)
The given equation is homogenous.
Robert Pina

Robert Pina

Beginner2022-01-02Added 42 answers

Simplifying
(2x+3y)dx+(2y+3x)dy=0
Reorder the terms for easier multiplication:
dx(2x+3y)+(2y+3x)dy=0
(2xdx+3ydx)+(2y+3x)dy=0
Reorder the terms:
(3dxy+2dx2)+(2y+3x)dy=0
(3dxy+2dx2)+(2y+3x)dy=0
Reorder the terms:
3dxy+2dx2+(3x+2y)dy=0
Reorder the terms for easier multiplication:
3dxy+2dx2+dy(3x+2y)=0
3dxy+2dx2+(3xdy+2ydy)=0
3dxy+2dx2+(3dxy+2dy2)=0
Reorder the terms:
3dxy+3dxy+2dx2+2dy2=0
Combine like terms: 3dxy+3dxy=6dxy
6dxy+2dx2+2dy2=0
Solving
karton

karton

Expert2022-01-09Added 613 answers

2x3y+(2y3x)dydx=0
2x3y+(2y3x)y=0
Verify that M(x,y)y=N(x,y)x: True
Find (x,y):(x,y)=y23xy+x2+c1
y23xy+x2+c1=c2
y23xy+x2=c1
Isolate y: y=3x+5x2+4c12,y=3x5x2+4c12
y=3x+5x2+c12,y=3x5x2+c12

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?