4.212   ODE No. 1212

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

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

Mathematica: cpu = 0.375548 (sec), leaf count = 33 \[ \text {DSolve}\left [x \left (a x^2+b\right ) y'(x)+f(x) y(x)+x^2 y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.016 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {f \left ( x \right ) {\it \_Y} \left ( x \right ) }{{x}^{2}}}+{\frac { \left ( a{x}^{2}+b \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{x}}+{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]