\[ y''(x)=-\frac {(a+2 b+3 x) y'(x)}{2 (a+x) (b+x)}-\frac {(a-b) y(x)}{4 (a+x)^2 (b+x)} \] ✓ Mathematica : cpu = 0.0918773 (sec), leaf count = 53
\[\left \{\left \{y(x)\to \frac {c_1 \sqrt {a-b}+c_2 \sqrt {b+x}}{\sqrt {a-b} \sqrt {\frac {a+x}{a-b}}}\right \}\right \}\]
✓ Maple : cpu = 0.043 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={1 \left ( \sqrt {x+b}{\it \_C1}+{\it \_C2} \right ) {\frac {1}{\sqrt {{\frac {x+a}{a-b}}}}}} \right \} \]