2.1348   ODE No. 1348

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

\[ y''(x)=-\frac {y(x) \left (a \left (x^4+1\right )+b x^2\right )}{x^4}-\frac {y'(x)}{x} \] Mathematica : cpu = 0.36644 (sec), leaf count = 34

\[\{\{y(x)\to c_1 \text {MathieuC}[-b,a,i \log (x)]+c_2 \text {MathieuS}[-b,a,i \log (x)]\}\}\] Maple : cpu = 2.386 (sec), leaf count = 73

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