3.372   ODE No. 372

\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-4\, \left ( y \left ( x \right ) \right ) ^{3}+ay \left ( x \right ) +b=0} \]

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

Mathematica: cpu = 0.003501 (sec), leaf count = 27 \[ \left \{\left \{y(x)\to \wp \left (x-c_1;a,b\right )\right \},\left \{y(x)\to \wp \left (x+c_1;a,b\right )\right \}\right \} \]

Maple: cpu = 0.499 (sec), leaf count = 271 \[ \left \{ y \left ( x \right ) ={\frac {1}{6}\sqrt [3]{27\,b+3\,\sqrt {-3 \,{a}^{3}+81\,{b}^{2}}}}+{\frac {a}{2}{\frac {1}{\sqrt [3]{27\,b+3\, \sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}}},y \left ( x \right ) =-{\frac {1}{12 }\sqrt [3]{27\,b+3\,\sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}-{\frac {a}{4}{ \frac {1}{\sqrt [3]{27\,b+3\,\sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}}}-{ \frac {i}{2}}\sqrt {3} \left ( {\frac {1}{6}\sqrt [3]{27\,b+3\,\sqrt {- 3\,{a}^{3}+81\,{b}^{2}}}}-{\frac {a}{2}{\frac {1}{\sqrt [3]{27\,b+3\, \sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}}} \right ) ,y \left ( x \right ) =-{ \frac {1}{12}\sqrt [3]{27\,b+3\,\sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}-{ \frac {a}{4}{\frac {1}{\sqrt [3]{27\,b+3\,\sqrt {-3\,{a}^{3}+81\,{b}^{ 2}}}}}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{6}\sqrt [3]{27\,b+3 \,\sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}-{\frac {a}{2}{\frac {1}{\sqrt [3]{ 27\,b+3\,\sqrt {-3\,{a}^{3}+81\,{b}^{2}}}}}} \right ) ,y \left ( x \right ) ={\it WeierstrassP} \left ( x+{\it \_C1},a,b \right ) \right \} \]