\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) ^{2}-ay \left ( x \right ) -b=0} \]
Mathematica: cpu = 0.773098 (sec), leaf count = 233 \[ \left \{\text {Solve}\left [\frac {3 (a y(x)+b)^2 \left (3 c_1-\frac {4 (a y(x)+b)^{3/2}}{a}\right ) \left (1-\frac {4 (a y(x)+b)^{3/2}}{3 a c_1}\right ) \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {5}{3};\frac {4 (b+a y(x))^{3/2}}{3 a c_1}\right ){}^2}{\left (4 (a y(x)+b)^{3/2}-3 a c_1\right ){}^2}=\left (c_2+x\right ){}^2,y(x)\right ],\text {Solve}\left [\frac {3 (a y(x)+b)^2 \left (\frac {4 (a y(x)+b)^{3/2}}{a}+3 c_1\right ) \left (\frac {4 (a y(x)+b)^{3/2}}{3 a c_1}+1\right ) \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {5}{3};-\frac {4 (b+a y(x))^{3/2}}{3 a c_1}\right ){}^2}{\left (4 (a y(x)+b)^{3/2}+3 a c_1\right ){}^2}=\left (c_2+x\right ){}^2,y(x)\right ]\right \} \]
Maple: cpu = 0.203 (sec), leaf count = 201 \[ \left \{ \int ^{y \left ( x \right ) }\!{a\sqrt {3}{\frac {1}{\sqrt {a \left ( 4\,{\it \_a}\,\sqrt {a{\it \_a}+b}a+4\,b\sqrt {a{\it \_a}+b}-{ \it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-3\,{\frac {a}{\sqrt {-3\,a \left ( 4\,{\it \_a}\,\sqrt {a{ \it \_a}+b}a+4\,b\sqrt {a{\it \_a}+b}-{\it \_C1} \right ) }}}{d{\it \_a }}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!3\,{\frac {a}{\sqrt {-3 \,a \left ( 4\,{\it \_a}\,\sqrt {a{\it \_a}+b}a+4\,b\sqrt {a{\it \_a}+b }-{\it \_C1} \right ) }}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{a\sqrt {3}{\frac {1}{\sqrt {a \left ( 4\,{\it \_a}\, \sqrt {a{\it \_a}+b}a+4\,b\sqrt {a{\it \_a}+b}-{\it \_C1} \right ) }}}} {d{\it \_a}}-x-{\it \_C2}=0,y \left ( x \right ) =-{\frac {b}{a}} \right \} \]