2.100   ODE No. 100

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

\[ a+x y'(x)+x y(x)^2=0 \] Mathematica : cpu = 0.00910829 (sec), leaf count = 157

\[\left \{\left \{y(x)\to -\frac {c_1 J_1\left (2 i \sqrt {-a} \sqrt {x}\right )+i \sqrt {-a} \sqrt {x} \left (c_1 J_0\left (2 i \sqrt {-a} \sqrt {x}\right )-c_1 J_2\left (2 i \sqrt {-a} \sqrt {x}\right )-2 J_0\left (2 i \sqrt {-a} \sqrt {x}\right )\right )}{2 x \left (J_1\left (2 i \sqrt {-a} \sqrt {x}\right )-c_1 J_1\left (2 i \sqrt {-a} \sqrt {x}\right )\right )}\right \}\right \}\]

Maple : cpu = 0.08 (sec), leaf count = 59

\[ \left \{ y \left ( x \right ) ={1\sqrt {a} \left ( {{\sl J}_{0}\left (2\,\sqrt {a}\sqrt {x}\right )}{\it \_C1}+{{\sl Y}_{0}\left (2\,\sqrt {a}\sqrt {x}\right )} \right ) {\frac {1}{\sqrt {x}}} \left ( {\it \_C1}\,{{\sl J}_{1}\left (2\,\sqrt {a}\sqrt {x}\right )}+{{\sl Y}_{1}\left (2\,\sqrt {a}\sqrt {x}\right )} \right ) ^{-1}} \right \} \]