2.534   ODE No. 534

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

\[ 4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0 \] Mathematica : cpu = 0.0629499 (sec), leaf count = 114

\[\left \{\left \{y(x)\to \frac {-\sqrt {2} \sqrt {c_1 x^3+3 c_1{}^2 x^2+3 c_1{}^3 x+c_1{}^4}-c_1{}^2}{3 c_1}\right \},\left \{y(x)\to \frac {\sqrt {2} \sqrt {c_1 x^3+3 c_1{}^2 x^2+3 c_1{}^3 x+c_1{}^4}-c_1{}^2}{3 c_1}\right \}\right \}\] Maple : cpu = 0.059 (sec), leaf count = 84

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