2.1847   ODE No. 1847

\[ y^{(3)}(x) \left (y'(x)^2+1\right )-3 y'(x) y''(x)^2=0 \] Mathematica : cpu = 0.204956 (sec), leaf count = 95


\[\left \{\left \{y(x)\to c_3-\frac {i \sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-1+c_2{}^2 c_1{}^2}}{c_1}\right \},\left \{y(x)\to \frac {i \sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-1+c_2{}^2 c_1{}^2}}{c_1}+c_3\right \}\right \}\] Maple : cpu = 0.336 (sec), leaf count = 49


\[y \relax (x ) = -\sqrt {-x^{2}-2 x c_{2}-c_{2}^{2}+c_{1}}+c_{3}\]