\[ y(x)^2 (a y(x)+b)+2 y(x) y''(x)-y'(x)^2=0 \] ✓ Mathematica : cpu = 1.77729 (sec), leaf count = 437
DSolve[y[x]^2*(b + a*y[x]) - Derivative[1][y][x]^2 + 2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \sqrt {2} \text {$\#$1}^{3/2} \sqrt {2+\frac {4 c_1}{\text {$\#$1} \left (-b+\sqrt {b^2+2 a c_1}\right )}} \sqrt {1-\frac {2 c_1}{\text {$\#$1} \left (b+\sqrt {b^2+2 a c_1}\right )}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {2} \sqrt {\frac {c_1}{\sqrt {b^2+2 a c_1}-b}}}{\sqrt {\text {$\#$1}}}\right )|\frac {b-\sqrt {b^2+2 a c_1}}{b+\sqrt {b^2+2 a c_1}}\right )}{\sqrt {\frac {c_1}{-b+\sqrt {b^2+2 a c_1}}} \sqrt {-\text {$\#$1} \left (\text {$\#$1}^2 a+2 \text {$\#$1} b-2 c_1\right )}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {i \sqrt {2} \text {$\#$1}^{3/2} \sqrt {2+\frac {4 c_1}{\text {$\#$1} \left (-b+\sqrt {b^2+2 a c_1}\right )}} \sqrt {1-\frac {2 c_1}{\text {$\#$1} \left (b+\sqrt {b^2+2 a c_1}\right )}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {2} \sqrt {\frac {c_1}{\sqrt {b^2+2 a c_1}-b}}}{\sqrt {\text {$\#$1}}}\right )|\frac {b-\sqrt {b^2+2 a c_1}}{b+\sqrt {b^2+2 a c_1}}\right )}{\sqrt {\frac {c_1}{-b+\sqrt {b^2+2 a c_1}}} \sqrt {-\text {$\#$1} \left (\text {$\#$1}^2 a+2 \text {$\#$1} b-2 c_1\right )}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.932 (sec), leaf count = 71
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+(a*y(x)+b)*y(x)^2=0,y(x))
\[\int _{}^{y \left (x \right )}-\frac {2}{\sqrt {-2 a \,\textit {\_a}^{3}-4 b \,\textit {\_a}^{2}+4 \textit {\_a} c_{1}}}d \textit {\_a} -x -c_{2} = 0\]