2.470   ODE No. 470

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

\[ x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0 \] Mathematica : cpu = 0.238876 (sec), leaf count = 143

\[\left \{\text {Solve}\left [\frac {1}{2} \log (y(x))-\frac {\sqrt {4 x^2 y(x)^2+x^6} \tanh ^{-1}\left (\frac {x^2}{\sqrt {x^4+4 y(x)^2}}\right )}{2 x \sqrt {x^4+4 y(x)^2}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {4 x^2 y(x)^2+x^6} \tanh ^{-1}\left (\frac {x^2}{\sqrt {x^4+4 y(x)^2}}\right )}{2 x \sqrt {x^4+4 y(x)^2}}+\frac {1}{2} \log (y(x))=c_1,y(x)\right ]\right \}\] Maple : cpu = 0.653 (sec), leaf count = 87

\[ \left \{ y \left ( x \right ) =-{\frac {i}{2}}{x}^{2},y \left ( x \right ) ={\frac {i}{2}}{x}^{2},y \left ( x \right ) =-{\frac {1}{4}\sqrt {-4\,{\it \_C1}\,{x}^{2}+{{\it \_C1}}^{2}}},y \left ( x \right ) ={\frac {1}{4}\sqrt {-4\,{\it \_C1}\,{x}^{2}+{{\it \_C1}}^{2}}},y \left ( x \right ) =-2\,{\frac {\sqrt {{\it \_C1}\,{x}^{2}+4}}{{\it \_C1}}},y \left ( x \right ) =2\,{\frac {\sqrt {{\it \_C1}\,{x}^{2}+4}}{{\it \_C1}}} \right \} \]