\[ \frac {1}{2} (a-b) y(x)+x^a y(x)^2+x^b+x y'(x)=0 \] ✓ Mathematica : cpu = 0.0398361 (sec), leaf count = 40
\[\left \{\left \{y(x)\to -x^{\frac {b-a}{2}} \tan \left (\frac {2 x^{\frac {a+b}{2}}}{a+b}-c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.053 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) =-{1\tan \left ( {\frac {1}{a+b} \left ( 2\,{x}^{a/2+b/2}+{\it \_C1}\, \left ( a+b \right ) \right ) } \right ) \left ( {x}^{{\frac {a}{2}}-{\frac {b}{2}}} \right ) ^{-1}} \right \} \]