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 = 0.0180585 (sec), leaf count = 40

\[\left \{\left \{y(x)\to \frac {3 \left (\sqrt {a} x\right )^{2/3}}{2^{2/3}}\right \},\left \{y(x)\to \frac {a+c_1{}^3 x}{c_1{}^2}\right \}\right \}\] Maple : cpu = 0.042 (sec), leaf count = 76

\[ \left \{ y \left ( x \right ) ={\frac {{{\it \_C1}}^{3}x+a}{{{\it \_C1}}^{2}}},y \left ( x \right ) ={\frac {3\,\sqrt [3]{2}}{2}\sqrt [3]{a{x}^{2}}},y \left ( x \right ) ={\frac {3\,\sqrt [3]{2} \left ( -1+i\sqrt {3} \right ) }{4}\sqrt [3]{a{x}^{2}}},y \left ( x \right ) =-{\frac {3\,\sqrt [3]{2} \left ( 1+i\sqrt {3} \right ) }{4}\sqrt [3]{a{x}^{2}}} \right \} \]