2.1123   ODE No. 1123

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

\[ -\left (2 a x^2+1\right ) y'(x)+b x^3 y(x)+x y''(x)=0 \] Mathematica : cpu = 0.0141401 (sec), leaf count = 53

\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x^2 \left (\sqrt {a^2-b}-a\right )} \left (c_2 e^{x^2 \sqrt {a^2-b}}+c_1\right )\right \}\right \}\]

Maple : cpu = 0.053 (sec), leaf count = 45

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2} \left ( \sqrt {{a}^{2}-b}+a \right ) }}}+{\it \_C2}\,{{\rm e}^{-{\frac {{x}^{2}}{2} \left ( \sqrt {{a}^{2}-b}-a \right ) }}} \right \} \]