\[ y''(x)=-\frac {y(x) \left (a \left (x^4+1\right )+b x^2\right )}{x^4}-\frac {y'(x)}{x} \] ✓ Mathematica : cpu = 0.337471 (sec), leaf count = 34
DSolve[Derivative[2][y][x] == -(((b*x^2 + a*(1 + x^4))*y[x])/x^4) - Derivative[1][y][x]/x,y[x],x]
\[\{\{y(x)\to c_1 \text {MathieuC}[-b,a,i \log (x)]+c_2 \text {MathieuS}[-b,a,i \log (x)]\}\}\] ✓ Maple : cpu = 0.188 (sec), leaf count = 73
dsolve(diff(diff(y(x),x),x) = -1/x*diff(y(x),x)-(b*x^2+a*(x^4+1))/x^4*y(x),y(x))
\[y \left (x \right ) = \mathit {HD}\left (0, 2 a +b , 0, 2 a -b , \frac {x^{2}+1}{x^{2}-1}\right ) \left (\left (\int \frac {1}{x \mathit {HD}\left (0, 2 a +b , 0, 2 a -b , \frac {x^{2}+1}{x^{2}-1}\right )^{2}}d x \right ) c_{2}+c_{1}\right )\]