4.281   ODE No. 1281

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

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

Mathematica: cpu = 0.020503 (sec), leaf count = 28 \[ \left \{\left \{y(x)\to \frac {c_1 e^x}{\sqrt {x}}+c_2 e^x \sqrt {x}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 19 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\,{{\rm e}^{x}}{\frac {1}{ \sqrt {x}}}}+{\it \_C2}\,\sqrt {x}{{\rm e}^{x}} \right \} \]