Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #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 bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### 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

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 bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### 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

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 bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### 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

Offline