\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-1/2\,{\frac { \left ( 3\,x+a+2\,b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( x+a \right ) \left ( x+b \right ) }}-1/4\,{\frac { \left ( a-b \right ) y \left ( x \right ) }{ \left ( x+a \right ) ^{2} \left ( x+b \right ) }}=0} \]
Mathematica: cpu = 0.081010 (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 = 0.015 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\sqrt {x+b}{\frac {1}{\sqrt {1 +{\frac {x+b}{a-b}}}}}}+{{\it \_C2}{\frac {1}{\sqrt {1+{\frac {x+b}{a- b}}}}}} \right \} \]