2.467   ODE No. 467

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

\[ y(x) y'(x)^2-4 x y'(x)+y(x)=0 \] Mathematica : cpu = 0.29527 (sec), leaf count = 226

\[\left \{\left \{y(x)\to \sqrt {x^2+\frac {2^{2/3} c_1{}^3 x}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-4096 c_1{}^3 x^9+768 c_1{}^6 x^6-48 c_1{}^9 x^3+c_1{}^{12}}-c_1{}^6}}+\frac {\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-4096 c_1{}^3 x^9+768 c_1{}^6 x^6-48 c_1{}^9 x^3+c_1{}^{12}}-c_1{}^6}}{2\ 2^{2/3}}+\frac {2\ 2^{2/3} x^4}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {-4096 c_1{}^3 x^9+768 c_1{}^6 x^6-48 c_1{}^9 x^3+c_1{}^{12}}-c_1{}^6}}}\right \}\right \}\] Maple : cpu = 0.084 (sec), leaf count = 148

\[\left \{-\frac {c_{1} x}{\left (\frac {8 x^{2}-4 y \left (x \right )^{2}-4 \sqrt {4 x^{2}-y \left (x \right )^{2}}\, x}{y \left (x \right )^{2}}\right )^{\frac {1}{3}} \left (\frac {2 x -\sqrt {4 x^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )^{\frac {1}{3}} y \left (x \right )}+x = 0, -\frac {c_{1} x}{\left (\frac {2 x^{2}-y \left (x \right )^{2}+\sqrt {4 x^{2}-y \left (x \right )^{2}}\, x}{y \left (x \right )^{2}}\right )^{\frac {1}{3}} \left (\frac {2 x +\sqrt {4 x^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )^{\frac {1}{3}} y \left (x \right )}+x = 0\right \}\]