2.1343   ODE No. 1343

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

\[ y''(x)=-\frac {y(x) \left ((1-a) a x^2-b (b+x)\right )}{x^4} \] Mathematica : cpu = 0.655982 (sec), leaf count = 0 , DifferentialRoot result

\[\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{\unicode {f818}''(\unicode {f817}) \unicode {f817}^4+\left (-a^2 \unicode {f817}^2+a \unicode {f817}^2-b \unicode {f817}-b^2\right ) \unicode {f818}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2\right \}\right )(x)\right \}\right \}\]

Maple : cpu = 0.161 (sec), leaf count = 62

\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( \left ( 2\,ax+b \right ) {{\sl I}_{a}\left ({\frac {b}{x}}\right )}+{{\sl I}_{a+1}\left ({\frac {b}{x}}\right )}b \right ) +{\it \_C2}\, \left ( \left ( 2\,ax+b \right ) {{\sl K}_{a}\left ({\frac {b}{x}}\right )}-{{\sl K}_{a+1}\left ({\frac {b}{x}}\right )}b \right ) \right \} \]