2.372   ODE No. 372

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

\[ \text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\text {Global$\grave { }$b}+\text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2-4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3=0 \] Mathematica : cpu = 0.00474725 (sec), leaf count = 27

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \wp \left (\text {Global$\grave { }$x}-c_1;\text {Global$\grave { }$a},\text {Global$\grave { }$b}\right )\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \wp \left (\text {Global$\grave { }$x}+c_1;\text {Global$\grave { }$a},\text {Global$\grave { }$b}\right )\right \}\right \}\]

Maple : cpu = 0.678 (sec), leaf count = 271

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