4.201   ODE No. 1201

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

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

Mathematica: cpu = 0.054007 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to \frac {c_1 e^{-2 x} (2 x+3)}{2 x^2}+\frac {c_2 \left (2 x^2-4 x+3\right )}{4 x^2}\right \}\right \} \]

Maple: cpu = 0.015 (sec), leaf count = 34 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( 2\,{x}^{2}-4 \,x+3 \right ) }{{x}^{2}}}+{\frac {{\it \_C2}\,{{\rm e}^{-2\,x}} \left ( 2\,x+3 \right ) }{{x}^{2}}} \right \} \]