Math Help - Messy differential equation

1. Messy differential equation

Hi,
I have a annoying differential equation that looks like:

$-p_i+\alpha _i+\frac{\gamma F_j\left[\gamma p_i-\gamma \alpha _i+\alpha _j\right]}{-1+\gamma ^2}+\left(-c_i+p_i\right) \left(-1+\frac{\gamma ^2 F_j'\left[\gamma p_i-\gamma \alpha _i+\alpha _j\right]}{-1+\gamma ^2}\right)=0$

where F is a cdf and F' is the pdf.

I would like to solve it for ${F_j\left[\gamma p_i-\gamma \alpha _i+\alpha _j\right]}$ when changing $p_i$.

However, I do not manage to find solutions to my problem as I have several variables ( ${F_j\left[\gamma p_i-\gamma \alpha _i+\alpha _j\right]}$) instead of just one variable F(pi)in the cfd.

Does anyone have an idea on how to attack it?

Thanks

2. as I have several variables instead of just one variable

...Change variables maybe?