2.1744 ODE No. 1744
\[ 2 y(x) y''(x)-y'(x)^2 \left (y'(x)^2+1\right )=0 \]
✓ Mathematica : cpu = 1.81559 (sec), leaf count = 505
DSolve[-(Derivative[1][y][x]^2*(1 + Derivative[1][y][x]^2)) + 2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-i e^{-c_1} \left (\frac {\left (\sqrt {\text {$\#$1}}-1\right ) \left (\sqrt {-1+e^{2 c_1}}-\sqrt {-1+\text {$\#$1} e^{2 c_1}}\right ) \left (-2 \text {$\#$1} e^{4 c_1}+e^{2 c_1} \left (\text {$\#$1}+\sqrt {\text {$\#$1}} \left (1+2 \sqrt {-1+e^{2 c_1}} \sqrt {-1+\text {$\#$1} e^{2 c_1}}\right )+1\right )-\sqrt {-1+e^{2 c_1}} \sqrt {-1+\text {$\#$1} e^{2 c_1}}-1\right )}{\left (\sqrt {\text {$\#$1}} \left (-e^{2 c_1}\right )+\sqrt {-1+e^{2 c_1}} \sqrt {-1+\text {$\#$1} e^{2 c_1}}+1\right ){}^2}+2 e^{-c_1} \tanh ^{-1}\left (\frac {e^{-c_1} \left (\sqrt {-1+e^{2 c_1}}-\sqrt {-1+\text {$\#$1} e^{2 c_1}}\right )}{\sqrt {\text {$\#$1}}-1}\right )\right )\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [i e^{-c_1} \left (\frac {\left (\sqrt {\text {$\#$1}}-1\right ) \left (\sqrt {-1+e^{2 c_1}}-\sqrt {-1+\text {$\#$1} e^{2 c_1}}\right ) \left (-2 \text {$\#$1} e^{4 c_1}+e^{2 c_1} \left (\text {$\#$1}+\sqrt {\text {$\#$1}} \left (1+2 \sqrt {-1+e^{2 c_1}} \sqrt {-1+\text {$\#$1} e^{2 c_1}}\right )+1\right )-\sqrt {-1+e^{2 c_1}} \sqrt {-1+\text {$\#$1} e^{2 c_1}}-1\right )}{\left (\sqrt {\text {$\#$1}} \left (-e^{2 c_1}\right )+\sqrt {-1+e^{2 c_1}} \sqrt {-1+\text {$\#$1} e^{2 c_1}}+1\right ){}^2}+2 e^{-c_1} \tanh ^{-1}\left (\frac {e^{-c_1} \left (\sqrt {-1+e^{2 c_1}}-\sqrt {-1+\text {$\#$1} e^{2 c_1}}\right )}{\sqrt {\text {$\#$1}}-1}\right )\right )\& \right ][x+c_2]\right \}\right \}\]
✓ Maple : cpu = 0.453 (sec), leaf count = 823
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2*(diff(y(x),x)^2+1)=0,y(x))
\[y \left (x \right ) = \frac {\left (\operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right )^{2} c_{1}^{2} \textit {\_Z}^{2}-4 \tan \left (\textit {\_Z} \right )^{2} c_{1} c_{2} \textit {\_Z} -4 \tan \left (\textit {\_Z} \right )^{2} c_{1} x \textit {\_Z} +4 \tan \left (\textit {\_Z} \right )^{2} c_{2}^{2}+8 \tan \left (\textit {\_Z} \right )^{2} x c_{2} +4 \tan \left (\textit {\_Z} \right )^{2} x^{2}+c_{1}^{2} \textit {\_Z}^{2}-4 c_{1} \textit {\_Z} c_{2} -4 c_{1} \textit {\_Z} x -c_{1}^{2}+4 c_{2}^{2}+8 c_{2} x +4 x^{2}\right ) c_{1} -2 x -2 c_{2} \right ) \tan \left (\operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right )^{2} c_{1}^{2} \textit {\_Z}^{2}-4 \tan \left (\textit {\_Z} \right )^{2} c_{1} c_{2} \textit {\_Z} -4 \tan \left (\textit {\_Z} \right )^{2} c_{1} x \textit {\_Z} +4 \tan \left (\textit {\_Z} \right )^{2} c_{2}^{2}+8 \tan \left (\textit {\_Z} \right )^{2} x c_{2} +4 \tan \left (\textit {\_Z} \right )^{2} x^{2}+c_{1}^{2} \textit {\_Z}^{2}-4 c_{1} \textit {\_Z} c_{2} -4 c_{1} \textit {\_Z} x -c_{1}^{2}+4 c_{2}^{2}+8 c_{2} x +4 x^{2}\right )\right )}{2}+\frac {c_{1}}{2}\]