\[ y''(x)=-\frac {(a+2 b+3 x) y'(x)}{2 (a+x) (b+x)}-\frac {(a-b) y(x)}{4 (a+x)^2 (b+x)} \] ✓ Mathematica : cpu = 0.0552439 (sec), leaf count = 62
\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {\frac {b+x}{a-b}+1}}+\frac {c_2 \sqrt {b+x}}{\sqrt {a-b} \sqrt {\frac {b+x}{a-b}+1}}\right \}\right \}\] ✓ Maple : cpu = 0.033 (sec), leaf count = 27
\[y \relax (x ) = \frac {\sqrt {x +b}\, c_{1}+c_{2}}{\sqrt {\frac {x +a}{a -b}}}\]