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 = 0.176915 (sec), leaf count = 73

\[\left \{\left \{y(x)\to c_1 \left (2 \left (a x+\frac {b}{2}\right ) I_a\left (\frac {b}{x}\right )+b I_{a+1}\left (\frac {b}{x}\right )\right )+c_2 \left (2 \left (a x+\frac {b}{2}\right ) K_a\left (\frac {b}{x}\right )-b K_{a+1}\left (\frac {b}{x}\right )\right )\right \}\right \}\] Maple : cpu = 0.325 (sec), leaf count = 58

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