How many solutions does the differential equation have?

Printable View

- Nov 9th 2013, 05:53 AMSuvadipfirst order ordinary differential equation
How many solutions does the differential equation have?

- Nov 9th 2013, 08:48 AMHallsofIvyRe: first order ordinary differential equation
First, is a very strange way to write . Is that what you meant?

If it is, then this is a separable equation that is easily solvable: .

What do you get when you integrate both sides? - Nov 9th 2013, 09:32 AMSuvadipRe: first order ordinary differential equation
Ya this is easily solvable. But how many solutions does it have? The answer was given as 2. But I cant understand how? It was set in an entrance exam.

- Nov 9th 2013, 10:04 AMHallsofIvyRe: first order ordinary differential equation
Start by

**solving**it! That should help you see what**solutions**there are!

Have you considered what would happen if y were**identically**0? - Nov 9th 2013, 06:59 PMSuvadipRe: first order ordinary differential equation
I have arrived at the solution . This is the only solution I got. Then how the no of solution is 2?

- Nov 9th 2013, 07:16 PMProve ItRe: first order ordinary differential equation
Did you even read HallsofIvy's last post? You can only solve the equation through dividing, which means you're making the assumption that . WHAT IF IT WAS?!?!

- Nov 9th 2013, 07:34 PMSuvadipRe: first order ordinary differential equation
So the two solutions are ?

- Nov 9th 2013, 07:48 PMProve ItRe: first order ordinary differential equation
Yes