\[ y^{(3)}(x) \left (y'(x)^2+1\right )-3 y'(x) y''(x)^2=0 \] ✓ Mathematica : cpu = 0.204956 (sec), leaf count = 95
DSolve[-3*Derivative[1][y][x]*Derivative[2][y][x]^2 + (1 + Derivative[1][y][x]^2)*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_3-\frac {i \sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-1+c_2{}^2 c_1{}^2}}{c_1}\right \},\left \{y(x)\to \frac {i \sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x-1+c_2{}^2 c_1{}^2}}{c_1}+c_3\right \}\right \}\] ✓ Maple : cpu = 0.336 (sec), leaf count = 49
dsolve((diff(y(x),x)^2+1)*diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)*diff(diff(y(x),x),x)^2=0,y(x))
\[y \left (x \right ) = -\sqrt {-x^{2}-2 x c_{2}-c_{2}^{2}+c_{1}}+c_{3}\]