2.1158   ODE No. 1158

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

\[ -y(x) \left (a b+b^2 x^2\right )+a y'(x)+x^2 y''(x)=0 \] Mathematica : cpu = 0.163164 (sec), leaf count = 43

\[\left \{\left \{y(x)\to c_2 e^{b x} \int _1^xe^{\frac {a}{K[1]}-2 b K[1]}dK[1]+c_1 e^{b x}\right \}\right \}\] Maple : cpu = 1.285 (sec), leaf count = 178

\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {\it HeunD} \left ( 4\,\sqrt {2}\sqrt {ab},-1-4\,\sqrt {2}\sqrt {ab},8\,\sqrt {2}\sqrt {ab},-4\,\sqrt {2}\sqrt {ab}+1,{ \left ( \sqrt {2}\sqrt {ab}x-a \right ) \left ( \sqrt {2}\sqrt {ab}x+a \right ) ^{-1}} \right ) {{\rm e}^{{\frac {-b{x}^{2}+a}{x}}}}{\it \_C1}+{\it HeunD} \left ( -4\,\sqrt {2}\sqrt {ab},-1-4\,\sqrt {2}\sqrt {ab},8\,\sqrt {2}\sqrt {ab},-4\,\sqrt {2}\sqrt {ab}+1,{ \left ( \sqrt {2}\sqrt {ab}x-a \right ) \left ( \sqrt {2}\sqrt {ab}x+a \right ) ^{-1}} \right ) {{\rm e}^{bx}}{\it \_C2} \right ) \right \} \]