4.225   ODE No. 1225

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

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

Mathematica: cpu = 0.032004 (sec), leaf count = 29 \[ \left \{\left \{y(x)\to c_2 \left (x \sinh ^{-1}(x)-\sqrt {x^2+1}\right )+c_1 x\right \}\right \} \]

Maple: cpu = 0.016 (sec), leaf count = 24 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\, \left ( {\it Arcsinh} \left ( x \right ) x-\sqrt {{x}^{2}+1} \right ) \right \} \]