4.58   ODE No. 1058

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{x}^{2} \left ( 1+x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( {x}^{4}-2 \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.899614 (sec), leaf count = 55 \[ \left \{\left \{y(x)\to c_2 e^{\frac {x^3}{3}} \int _1^x e^{\frac {K[1]^4}{4}-\frac {K[1]^3}{3}} \, dK[1]+c_1 e^{\frac {x^3}{3}}\right \}\right \} \]

Maple: cpu = 0.093 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{3}}{3} }}}+{\it \_C2}\,{{\rm e}^{{\frac {{x}^{3}}{3}}}}\int \!{{\rm e}^{{ \frac {{x}^{4}}{4}}-{\frac {{x}^{3}}{3}}}}\,{\rm d}x \right \} \]