\[ -a y(x)-b+y''(x)^2=0 \] ✓ Mathematica : cpu = 0.59255 (sec), leaf count = 201
\[\left \{\text {Solve}\left [\frac {(a y(x)+b)^2 \left (1-\frac {4 (a y(x)+b)^{3/2}}{3 a c_1}\right ) \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {5}{3};\frac {4 (b+a y(x))^{3/2}}{3 a c_1}\right ){}^2}{a^2 \left (-\frac {4 (a y(x)+b)^{3/2}}{3 a}+c_1\right )}=(x+c_2){}^2,y(x)\right ],\text {Solve}\left [\frac {(a y(x)+b)^2 \left (1+\frac {4 (a y(x)+b)^{3/2}}{3 a c_1}\right ) \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {5}{3};-\frac {4 (b+a y(x))^{3/2}}{3 a c_1}\right ){}^2}{a^2 \left (\frac {4 (a y(x)+b)^{3/2}}{3 a}+c_1\right )}=(x+c_2){}^2,y(x)\right ]\right \}\] ✓ Maple : cpu = 1.428 (sec), leaf count = 173
\[ \left \{ \int ^{y \left ( x \right ) }\!{\sqrt {3}a{\frac {1}{\sqrt {a \left ( 4\,{\it \_a}\,\sqrt {{\it \_a}\,a+b}a+4\,b\sqrt {{\it \_a}\,a+b}-{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-3\,{\frac {a}{\sqrt {-12\,a \left ( \left ( {\it \_a}\,a+b \right ) ^{3/2}-{\it \_C1}/4 \right ) }}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!3\,{\frac {a}{\sqrt {-12\,a \left ( \left ( {\it \_a}\,a+b \right ) ^{3/2}-{\it \_C1}/4 \right ) }}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\sqrt {3}a{\frac {1}{\sqrt {a \left ( 4\,{\it \_a}\,\sqrt {{\it \_a}\,a+b}a+4\,b\sqrt {{\it \_a}\,a+b}-{\it \_C1} \right ) }}}}{d{\it \_a}}-x-{\it \_C2}=0,y \left ( x \right ) =-{\frac {b}{a}} \right \} \]