# Abel's Formula

1. Mar 13, 2014

### physics=world

1. Use Abel's Formula to find the Wronskian of two solutions of the given differential equation
without solving the equation.

x2y" - x(x+2)y' + (t + 2)y = 0

2.

Abel's Formula

W(y1, y2)(x) = ce-∫p(x)dx

3.

I put it in the form of

y" + p(x)y' + q(x)y = 0

to find my p(x) to use for Abel's formula

p(x) = - (x+2 / x)

this would give:

W(y1, y2)(x) = ce-∫(-)(x+2 / x)dx

I'm not sure if I'm going in the right direction. I need some help.

Last edited by a moderator: Mar 13, 2014
2. Mar 13, 2014

### Staff: Mentor

Your use of parentheses is commendable, although you have them in the wrong place here and below.
You should have p(x) = -(x + 2)/x

What you wrote is the same as $-(x + \frac 2 x)$.
This seems OK to me (aside from the parentheses thing). Are you having trouble with the integration?

3. Mar 13, 2014

### physics=world

After integrating I get:

ce(x) + 2ln(x)

4. Mar 13, 2014

### Staff: Mentor

You should simplify that.
I believe that c is W(y1(x), y2(x))(x0). IOW, the Wronskian of the two functions, evaluated at some initial x value.