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## #1 2012-10-10 15:30:38

yago.dorea
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### 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?

## #2 2012-10-10 17:54:12

bob bundy
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### 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

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #3 2012-10-10 18:03:50

yago.dorea
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### Re: First order differential equation

How exactly do you separate?

## #4 2012-10-10 18:07:18

bob bundy
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### Re: First order differential equation

hi

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #5 2012-10-10 18:23:51

yago.dorea
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### 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 (2012-10-10 18:25:23)

## #6 2012-10-11 05:48:31

bob bundy
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### 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

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei