2.1306   ODE No. 1306

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

\[ y(x) \left (a x^2+a+b x\right )+x^2 y'(x)+x^3 y''(x)=0 \] Mathematica : cpu = 0.940047 (sec), leaf count = 0 , DifferentialRoot result

\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}''(\unicode {f817}) \unicode {f817}^3+\unicode {f818}'(\unicode {f817}) \unicode {f817}^2+\left (a \unicode {f817}^2+b \unicode {f817}+a\right ) \unicode {f818}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2\right \}\right )(x)\right \}\right \}\]

Maple : cpu = 1.13 (sec), leaf count = 69

\[ \left \{ y \left ( x \right ) ={\it HeunD} \left ( 0,8\,a+4\,b,0,8\,a-4\,b,{\frac {1+x}{x-1}} \right ) \left ( \int \!{\frac {1}{x} \left ( {\it HeunD} \left ( 0,8\,a+4\,b,0,8\,a-4\,b,{\frac {1+x}{x-1}} \right ) \right ) ^{-2}}\,{\rm d}x{\it \_C2}+{\it \_C1} \right ) \right \} \]