Inconsistent solution to nonlinear first order differential equation.

Question

I am trying to solve the following first order differential equation, $$ y'(x)=-\frac{a}{x}-\frac{b}{y(x)} $$ with boundary condition of, $$ y(c)=d $$ The above equation is the Abel's equation which has a complicated and lengthy method of solving it. I am looking for something that is simple to begin with. I am not sure if my approach is correct, but my attempted solution is by differentiating it and solving, $$ y''=\frac{a}{x^2}+\frac{by'}{y^2} $$ The above equation is still nonlinear but it has an obvious solution which is $$y=Ax $$ where A is an arbitrary constant. Plugging into second order differential equation yields, $$ 0= \frac{a}{x^2}+\frac{Ab}{A^2x^2} $$ and solving for A gives $$A= \frac{-b}{a} $$ However, if I use the solution to first order equation I will get inconsistent results or $$ -b/a=0 $$ Does that mean that differentiating approach is incorrect way to start solving or I missed some steps in solving it? Any other suggestions are appreciated.