• Support PF! Buy your school textbooks, materials and every day products Here!

Solving an ODE

  • Thread starter cragar
  • Start date
  • #1
2,544
2

Homework Statement


Ay'+Bxy=Cy
y=f(x)
A,B,C are real constants

The Attempt at a Solution


This kinda looks like a Bernoulli equation but not really.
I thought about using an integrating factor but there is function of x on the right side.
If I tried undetermined coefficients what would my guess function be.
 

Answers and Replies

  • #2
It seems like you could solve this by first manipulating to get [tex]y' + \frac{Bx-C}{A}y = 0[/tex] at which point you now have an ODE of the form [tex]y' + P(x)y = Q(x)[/tex] and there is a general way to solve such ODEs.
 
  • #3
2,544
2
where Q(x)=0 and then use an integrating factor.
 
  • #4
Yep, seems like that oughta work
 
  • #5
2,544
2
if you do that you get y=0.
 
  • #6
ehild
Homework Helper
15,395
1,802
It seems like you could solve this by first manipulating to get [tex]y' + \frac{Bx-C}{A}y = 0[/tex]
or [tex]y' = -\frac{Bx-C}{A}y [/tex]

which is separable. [tex]\frac{y'}{y} = -\frac{Bx-C}{A}[/tex].

ehild
 
  • #7
2,544
2
wow cant believe I missed that , thanks for the help
ok so I would get
[itex] ln(y)= \frac{-1}{A}(\frac{Bx^2}{2}-Cx)+F [/itex]
F= integration constant
then I just raise each side to e and I will have y
 
  • #8
ehild
Homework Helper
15,395
1,802
Exactly. It will be a bit simpler if you eliminate the minus sign in front of the parentheses,

[tex]\ln(y)=\frac{1}{A}(Cx-B\frac{x^2}{2})+F[/tex]

ehild
 

Related Threads for: Solving an ODE

  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
4
Views
920
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
12
Views
2K
Top