Solve a second-order differential equation

[Sara_76]

TL;DR Summary

Can I find help in solving this equation

 

[BvU]

Hello sara, $\qquad$ $\qquad$ !

The solution is given: (24)

 

[Sara_76]

welcome

I want to know how to solve

 

[BvU]

The more I look at it, the stranger the whole thing seems to be.
$-{1\over a } {d\Psi(y)\over dx }\$ -- a typo ($x$ should be $y$) ?
and (in 24) $\ \ \ e_1^{-\sqrt B y} \$ -- what is the subscipt 1 ?

Looks as if they tried $y^p e^q$ and swept the leftovers in an $F_1$ (with three arguments ?) ...

 

[Sara_76]

for −1/adΨ(y)/dx
It's a mistake in writing (It's y, not x )

 

[BvU]

Where does this come from and what is it leading to ?