2.457   ODE No. 457

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

\[ x^4 y'(x)^2-x y'(x)-y(x)=0 \] Mathematica : cpu = 0.243138 (sec), leaf count = 118

\[\left \{\text {Solve}\left [-\frac {x \sqrt {4 x^2 y(x)+1} \tanh ^{-1}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ],\text {Solve}\left [\frac {x \sqrt {4 x^2 y(x)+1} \tanh ^{-1}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ]\right \}\] Maple : cpu = 3.827 (sec), leaf count = 45

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