4.352   ODE No. 1352

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

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

Mathematica: cpu = 0.013002 (sec), leaf count = 89 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {\sqrt {b} \left (-\frac {\sqrt {a^2-b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{x}}+c_2 e^{-\frac {\sqrt {b} \left (\frac {\sqrt {a^2-b}}{\sqrt {b}}-\frac {a}{\sqrt {b}}\right )}{x}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {1}{x} \left ( a-\sqrt {{a}^{2}-b} \right ) }}}+{\it \_C2}\,{{\rm e}^{{\frac { 1}{x} \left ( \sqrt {{a}^{2}-b}+a \right ) }}} \right \} \]