\[ k (-a+y(x)+x) (-b+y(x)+x)+(x-a) (x-b) y'(x)+y(x)^2=0 \] ✓ Mathematica : cpu = 0.270429 (sec), leaf count = 133
\[\left \{\left \{y(x)\to \frac {1}{2} \sqrt {\frac {-a^2 k^2+2 a b k^2-b^2 k^2}{(k+1)^2}} \tan \left (\frac {(k+1) \sqrt {\frac {-a^2 k^2+2 a b k^2-b^2 k^2}{(k+1)^2}} (\log (x-b)-\log (x-a))}{2 (a-b)}+c_1\right )-\frac {-a k-b k+2 k x}{2 (k+1)}\right \}\right \}\] ✓ Maple : cpu = 0.202 (sec), leaf count = 58
\[ \left \{ y \left ( x \right ) ={\frac { \left ( {\it \_C1}\, \left ( a-x \right ) \left ( a-x \right ) ^{k}+ \left ( b-x \right ) ^{k} \left ( b-x \right ) \right ) k}{ \left ( k+1 \right ) \left ( {\it \_C1}\, \left ( a-x \right ) ^{k}+ \left ( b-x \right ) ^{k} \right ) }} \right \} \]