# Wronskian Second Solution/Differential Equations

1. Feb 26, 2009

### tracedinair

1. The problem statement, all variables and given/known data

Given that Φ2 = Φ1 * ∫ e^(-∫a(x)dx)) / (Φ1)^2 dx

and Φ1 = cos(ln(x)), a = 1/x, solve for Φ2.

2. Relevant equations

3. The attempt at a solution

Φ2 = cos(ln(x)) * ∫ e^(-∫1/x dx)) / cos^(2)(ln(x)) dx

= cos(ln(x)) * ∫ e^(-ln(x)) / cos^(2)(ln(x)) dx

= cos(ln(x)) * - ∫ x / cos^(2)(ln(x)) dx

My problem begins here with trying to solve for that integral. I don't have the slightest idea where to begin, except maybe integration by parts.

2. Feb 26, 2009

### djeitnstine

I believe you have expanded your brackets in the exponential wrong $$e^{-ln(x)}$$ does not equal $$-x$$ but rather $$e^{ln(x^{-1})}$$ which is of course $$\frac{1}{x}$$ in which case a simple u substitution will work

3. Feb 26, 2009

### tracedinair

Thanks for catching that mistake.