2.1689   ODE No. 1689

\[ x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0 \] Mathematica : cpu = 0.269586 (sec), leaf count = 104


\[\left \{\left \{y(x)\to -i x \log \left (\frac {\frac {e^{c_2}}{x}-\frac {\sqrt {e^{2 c_2}-8 i c_1 x^2}}{x}}{4 c_1}\right )\right \},\left \{y(x)\to -i x \log \left (\frac {\frac {\sqrt {e^{2 c_2}-8 i c_1 x^2}}{x}+\frac {e^{c_2}}{x}}{4 c_1}\right )\right \}\right \}\] Maple : cpu = 0.949 (sec), leaf count = 37


\[y \relax (x ) = \left (-\arctan \left (\frac {1}{\sqrt {c_{1} x^{2}-1}}\right )+c_{2}\right ) x\]