2.541   ODE No. 541

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

\[ y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0 \] Mathematica : cpu = 0.0312306 (sec), leaf count = 39

\[\left \{\left \{y(x)\to -\sqrt {2 c_1 x+c_1{}^3}\right \},\left \{y(x)\to \sqrt {2 c_1 x+c_1{}^3}\right \}\right \}\] Maple : cpu = 0.533 (sec), leaf count = 103

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