2.1689   ODE No. 1689

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0 \] Mathematica : cpu = 0.246973 (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 = 0.367 (sec), leaf count = 37

\[ \left \{ y \left ( x \right ) = \left ( -\arctan \left ( {\frac {1}{\sqrt {{\it \_C1}\,{x}^{2}-1}}} \right ) +{\it \_C2} \right ) x,y \left ( x \right ) = \left ( \arctan \left ( {\frac {1}{\sqrt {{\it \_C1}\,{x}^{2}-1}}} \right ) +{\it \_C2} \right ) x \right \} \]