1st O.D.E, homogenous but with constants

  • Thread starter Thread starter niceperson
  • Start date Start date
  • Tags Tags
    Constants
Click For Summary
SUMMARY

The discussion revolves around solving the differential equation y'=(x+y-1)/(x-y-2) using the substitution y=vx. The user attempts to manipulate the equation but struggles to separate the variables after substitution. A suggestion is made to verify the solution, indicating the importance of accuracy in the problem-solving process. The conversation highlights the challenges faced when applying substitution methods in differential equations.

PREREQUISITES
  • Understanding of first-order differential equations
  • Familiarity with substitution methods in calculus
  • Knowledge of variable separation techniques
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study methods for solving first-order differential equations
  • Learn about substitution techniques in differential equations
  • Research variable separation methods in calculus
  • Practice solving differential equations with varying complexity
USEFUL FOR

Students studying calculus, mathematicians focusing on differential equations, and educators teaching advanced mathematics concepts.

niceperson
Messages
5
Reaction score
0

Homework Statement



solve: y'=(x+y-1)/(x-y-2) i.e

Homework Equations





The Attempt at a Solution



let y=vx
thus
y'=v'x+v

by substitution:

v'x+v=(1+y/x-1/x)/(1-y/x-2/x)=(1+v-1/x)/(1-v-2/x)

v'x=(1-1/x+v^2+2v/x)/(1-v-2/x)

still can't separate the variables...any ideas?

thanksx
 
Physics news on Phys.org
thanks dick does work!
 
Uh, are you sure? I tried it again after I posted, and realized I'd made a mistake and deleted the post so it wouldn't confuse anyone. Just double check, ok?
 
Last edited:

Similar threads

Replies
2
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
7
Views
1K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 12 ·
Replies
12
Views
4K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K