\[ -a y(x)-b+y''(x)^2=0 \] ✓ Mathematica : cpu = 0.76088 (sec), leaf count = 201
DSolve[-b - a*y[x] + Derivative[2][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {(a y(x)+b)^2 \left (1-\frac {4 (a y(x)+b)^{3/2}}{3 a c_1}\right ) \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {5}{3};\frac {4 (b+a y(x))^{3/2}}{3 a c_1}\right ){}^2}{a^2 \left (-\frac {4 (a y(x)+b)^{3/2}}{3 a}+c_1\right )}=(x+c_2){}^2,y(x)\right ],\text {Solve}\left [\frac {(a y(x)+b)^2 \left (1+\frac {4 (a y(x)+b)^{3/2}}{3 a c_1}\right ) \, _2F_1\left (\frac {1}{2},\frac {2}{3};\frac {5}{3};-\frac {4 (b+a y(x))^{3/2}}{3 a c_1}\right ){}^2}{a^2 \left (\frac {4 (a y(x)+b)^{3/2}}{3 a}+c_1\right )}=(x+c_2){}^2,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.559 (sec), leaf count = 173
dsolve(diff(diff(y(x),x),x)^2-a*y(x)-b=0,y(x))
\[y \left (x \right ) = -\frac {b}{a}\]