2.533   ODE No. 533

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

\[ a+x y'(x)^3-y(x) y'(x)^2=0 \] Mathematica : cpu = 0.0049101 (sec), leaf count = 16

\[\left \{\left \{y(x)\to \frac {a}{c_1{}^2}+c_1 x\right \}\right \}\] Maple : cpu = 0.197 (sec), leaf count = 76

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