# Thread: Initial Value problem

1. ## Initial Value problem

Hi, i have this initial value problem for y(0) = 1 and the following equation :

dy/dt = ( y + 1/y ) * 1/2

The question asks to prove the solution is:

y = sqrt( 2*exp(x) - 1 )

I am confused as to where the extra variable x comes from ?
any help apprieciated, thnks in advance

2. Originally Posted by Richyie
Hi, i have this initial value problem for y(0) = 1 and the following equation :

dy/dt = ( y + 1/y ) * 1/2

The question asks to prove the solution is:

y = sqrt( 2*exp(x) - 1 )

I am confused as to where the extra variable x comes from ?
any help apprieciated, thnks in advance
Use:

$y = \sqrt{ 2\exp(t) - 1 }$

and you don't have to solve the IVP just show that this function satisfies both the DE and the initial condition.

CB

3. hi, thanks for the reply!

im still abit confused to why in the question X is used instread of t, how are they interchangable ?

4. Originally Posted by Richyie
hi, thanks for the reply!

im still abit confused to why in the question X is used instread of t, how are they interchangable ?
x and t are dummy variables it does not matter what they are called as long as you use the same name all of the time.

The question has a typo it should have used t in the second equation.

CB

5. thanks ! , that was what was confusing me origionally