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 = 0.380489 (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 = 0.253 (sec), leaf count = 73

\[\left \{y \left (x \right ) = \left (c_{2} \left (\int \frac {1}{x \mathit {HD}\left (0, 2 a +b , 0, 2 a -b , \frac {x^{2}+1}{x^{2}-1}\right )^{2}}d x \right )+c_{1}\right ) \mathit {HD}\left (0, 2 a +b , 0, 2 a -b , \frac {x^{2}+1}{x^{2}-1}\right )\right \}\]