4.193   ODE No. 1193

\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +x \left ( 1+x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( x-9 \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.048506 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to \frac {c_1 ((x-8) x+20)}{x^3}-\frac {c_2 e^{-x} \left (x^3+9 x^2+36 x+60\right )}{x^3}\right \}\right \} \]

Maple: cpu = 0.032 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {x}^{2}-8\,x+ 20 \right ) }{{x}^{3}}}+{\frac {{\it \_C2}\,{{\rm e}^{-x}} \left ( {x}^{ 3}+9\,{x}^{2}+36\,x+60 \right ) }{{x}^{3}}} \right \} \]