4.401   ODE No. 1401

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

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

Mathematica: cpu = 0.013002 (sec), leaf count = 93 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {\sqrt {b} \left (-\frac {\sqrt {a^2-4 b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{4 x^2}}+c_2 e^{-\frac {\sqrt {b} \left (\frac {\sqrt {a^2-4 b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{4 x^2}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 45 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {1}{4\,{x}^ {2}} \left ( -a+\sqrt {{a}^{2}-4\,b} \right ) }}}+{\it \_C2}\,{{\rm e}^{ {\frac {1}{4\,{x}^{2}} \left ( a+\sqrt {{a}^{2}-4\,b} \right ) }}} \right \} \]