I have been trying to work out how to solve this example question I found in a recommended text,

Everywhere I've been reading starts with since y=eta(x) is a particular solution then y=eta(x) + u is a general solution, but the question doesn't state eta(x) as a particular solution, is that a problem?

Anyway in this question is the way to go simply subbing in y = eta + 1/si then noting that all the lone eta components cancel since they are a solution themselves.

But when I do that,

I end up with something like

and I can't rearrange it to form the equation which si solves,

any idea on what i've done wrong?

p.s. Has latex been removed from forum?