I'm currently working on a multi-step problem and got stuck. I've worked with ODEs before, but this time I was asked to multiply by $v(x)$, where $v(0) = 0$, and then reduce the problem to an integral.
I've recognized that I'm dealing with a boundary value problem, but I've never worked with those before and the papers I've read haven't been much help.
Integrate the equation and use by parts for LHS of (2). The BC's allow the boundary term to vanish giving (3).