5.62   ODE No. 1510

\[ \boxed { {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( a{x}^{2\,\nu }+1-{\nu }^{2} \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( b{x}^{3\,\nu }+a \left ( \nu -1 \right ) {x}^{2\,\nu }+{\nu }^{2}-1 \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.052007 (sec), leaf count = 60 \[ \text {DSolve}\left [y(x) \left (a (\nu -1) x^{2 \nu }+b x^{3 \nu }+\nu ^2-1\right )+x \left (a x^{2 \nu }-\nu ^2+1\right ) y'(x)+x^3 y^{(3)}(x)=0,y(x),x\right ] \]

Maple: cpu = 0.078 (sec), leaf count = 74 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {x}^{3}{ \frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) + \left ( {x}^{2\,\nu }ax-{\nu }^{2}x+x \right ) {\frac {\rm d}{{\rm d}x}}{ \it \_Y} \left ( x \right ) + \left ( {x}^{2\,\nu }a\nu -a{x}^{2\,\nu }+b{x} ^{3\,\nu }+{\nu }^{2}-1 \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]