4.405   ODE No. 1405

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) ={\frac { \left ( 2\,{x}^{2}+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{{x}^{3}}}-1/4\,{\frac { \left ( a{x}^{4}+10\,{x}^{2}+1 \right ) y \left ( x \right ) }{{x}^{6}}}=0} \]

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

Mathematica: cpu = 0.075510 (sec), leaf count = 77 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {1}{4 x^2}} x^{\frac {3}{2}-\frac {\sqrt {9-a}}{2}}+\frac {c_2 e^{-\frac {1}{4 x^2}} x^{\frac {\sqrt {9-a}}{2}+\frac {3}{2}}}{\sqrt {9-a}}\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {3}{2}}+{\frac {1 }{2}\sqrt {-a+9}}}{{\rm e}^{-{\frac {1}{4\,{x}^{2}}}}}+{\it \_C2}\,{x} ^{{\frac {3}{2}}-{\frac {1}{2}\sqrt {-a+9}}}{{\rm e}^{-{\frac {1}{4\,{ x}^{2}}}}} \right \} \]