\[ \boxed { \left ( ay \left ( x \right ) -bx \right ) ^{2} \left ( {a}^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+{b}^{2} \right ) -{c}^{2} \left ( a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +b \right ) ^{2}=0} \]
Mathematica: cpu = 1.717718 (sec), leaf count = 100 \[ \left \{\left \{y(x)\to \frac {b c_1}{a}-\frac {\sqrt {2 b^2 c_1 x-b^2 c_1^2+b^2 \left (-x^2\right )+c^2}}{a}\right \},\left \{y(x)\to \frac {\sqrt {2 b^2 c_1 x-b^2 c_1^2+b^2 \left (-x^2\right )+c^2}}{a}+\frac {b c_1}{a}\right \}\right \} \]
Maple: cpu = 0.890 (sec), leaf count = 195 \[ \left \{ y \left ( x \right ) ={\frac {bx-\sqrt {2}c}{a}},y \left ( x \right ) ={\frac {bx+\sqrt {2}c}{a}},y \left ( x \right ) ={\frac {1}{a} \left ( {\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {a}{ \left ( 2 \,{{\it \_a}}^{2}{a}^{2}-4\,{c}^{2} \right ) b} \left ( -{{\it \_a}}^{2} {a}^{2}+2\,{c}^{2}+\sqrt {-{a}^{2}{{\it \_a}}^{2} \left ( {{\it \_a}}^{ 2}{a}^{2}-2\,{c}^{2} \right ) } \right ) }{d{\it \_a}}+{\it \_C1} \right ) a+bx \right ) },y \left ( x \right ) ={\frac {1}{a} \left ( {\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!-{\frac {a}{ \left ( 2\,{{\it \_a} }^{2}{a}^{2}-4\,{c}^{2} \right ) b} \left ( {{\it \_a}}^{2}{a}^{2}-2\,{c }^{2}+\sqrt {-{a}^{2}{{\it \_a}}^{2} \left ( {{\it \_a}}^{2}{a}^{2}-2\, {c}^{2} \right ) } \right ) }{d{\it \_a}}+{\it \_C1} \right ) a+bx \right ) } \right \} \]