\[ \boxed { \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,axy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 1-a \right ) \left ( y \left ( x \right ) \right ) ^{2}+a{x}^{2}+ \left ( a-1 \right ) b=0} \]
Mathematica: cpu = 1.033131 (sec), leaf count = 79 \[ \left \{\left \{y(x)\to -\sqrt {-2 a c_1 x+a c_1^2+b+2 c_1 x-c_1^2-x^2}\right \},\left \{y(x)\to \sqrt {-2 a c_1 x+a c_1^2+b+2 c_1 x-c_1^2-x^2}\right \}\right \} \]
Maple: cpu = 1.107 (sec), leaf count = 251 \[ \left \{ y \left ( x \right ) =\sqrt {-a{x}^{2}+b},y \left ( x \right ) ={ \frac {1}{a}\sqrt {-{a}^{2}{x}^{2}-2\,a\sqrt {{\it \_C1}\,{a}^{2}-{a}^ {2}b-{\it \_C1}\,a+ab}x+{\it \_C1}\,a+{a}^{2}b-ab}},y \left ( x \right ) ={\frac {1}{a}\sqrt {-{a}^{2}{x}^{2}+2\,a\sqrt {{\it \_C1}\,{ a}^{2}-{a}^{2}b-{\it \_C1}\,a+ab}x+{\it \_C1}\,a+{a}^{2}b-ab}},y \left ( x \right ) =-\sqrt {-a{x}^{2}+b},y \left ( x \right ) =-{\frac {1 }{a}\sqrt {-{a}^{2}{x}^{2}-2\,a\sqrt {{\it \_C1}\,{a}^{2}-{a}^{2}b-{ \it \_C1}\,a+ab}x+{\it \_C1}\,a+{a}^{2}b-ab}},y \left ( x \right ) =-{ \frac {1}{a}\sqrt {-{a}^{2}{x}^{2}+2\,a\sqrt {{\it \_C1}\,{a}^{2}-{a}^ {2}b-{\it \_C1}\,a+ab}x+{\it \_C1}\,a+{a}^{2}b-ab}} \right \} \]