\[ a y'(x)^2+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.530574 (sec), leaf count = 104
DSolve[b*y[x] + a*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {\sqrt {2} a}{\sqrt {2 e^{-2 a K[1]} c_1 a^2-2 b K[1] a+b}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt {2} a}{\sqrt {2 e^{-2 a K[2]} c_1 a^2-2 b K[2] a+b}}dK[2]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.043 (sec), leaf count = 79
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)^2+b*y(x)=0,y(x))
\[\int _{}^{y \left (x \right )}-\frac {2 a}{\sqrt {4 \,{\mathrm e}^{-2 a \textit {\_a}} c_{1} a^{2}-4 \textit {\_a} a b +2 b}}d \textit {\_a} -x -c_{2} = 0\]