Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2012-10-09 16:30:38
- yago.dorea
- Member
- Registered: 2012-09-09
- Posts: 6
First order differential equation
I want to solve the following ODE:
(1 + t²)y' = ty(1 + y²) where y = y(t).
If I try to solve it by separation, I get complex roots, but I'm not trained yet to deal with them. 
What should I do?
Live long and prosper.
Offline
#2 2012-10-09 18:54:12
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,632
Re: First order differential equation
hi yago.dorea
Welcome to the forum.
Separation, the partial fractions for y and 'function of a function' for t.
I'm getting
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
Offline
#3 2012-10-09 19:03:50
- yago.dorea
- Member
- Registered: 2012-09-09
- Posts: 6
Re: First order differential equation
How exactly do you separate?
Live long and prosper.
Offline
#4 2012-10-09 19:07:18
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,632
Re: First order differential equation
hi
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#5 2012-10-09 19:23:51
- yago.dorea
- Member
- Registered: 2012-09-09
- Posts: 6
Re: First order differential equation
Okay, but the result of this equation is that y(t) is a complex function ( y² = sqrt(-(t²+1))/t ). Can this be the right answer?
Last edited by yago.dorea (2012-10-09 19:25:23)
Live long and prosper.
Offline
#6 2012-10-10 06:48:31
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,632
Re: First order differential equation
Go back to
Let's say 2C = lnA
Now you should have been given values of y and t to enable you to work out A.
For what follows I'm going to assume lnA = 1
So it does seem to give that function.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
Pages: 1