4.148   ODE No. 1148

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

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

Mathematica: cpu = 0.009501 (sec), leaf count = 77 \[ \left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \left (\frac {1}{\sqrt {a}}-\frac {\sqrt {1-4 a}}{\sqrt {a}}\right ) \sqrt {a}}+c_2 x^{\frac {1}{2} \left (\frac {\sqrt {1-4 a}}{\sqrt {a}}+\frac {1}{\sqrt {a}}\right ) \sqrt {a}}\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {1}{2}}+{\frac {1 }{2}\sqrt {1-4\,a}}}+{\it \_C2}\,{x}^{{\frac {1}{2}}-{\frac {1}{2} \sqrt {1-4\,a}}} \right \} \]