2.372   ODE No. 372

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

\[ a y(x)+b+y'(x)^2-4 y(x)^3=0 \] Mathematica : cpu = 0.0038499 (sec), leaf count = 27

\[\{\{y(x)\to \wp (x-c_1;a,b)\},\{y(x)\to \wp (x+c_1;a,b)\}\}\] Maple : cpu = 0.05 (sec), leaf count = 232

\[\left \{y \left (x \right ) = -\frac {3 a +\left (-3 i a +i \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {3 a +\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}}{6 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}}, y \left (x \right ) = \frac {-3 i \sqrt {3}\, a -3 a +i \sqrt {3}\, \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}-\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}}, y \left (x \right ) = \WeierstrassP \left (c_{1}+x , a , b\right )\right \}\]