\[ y''(x)=\frac {(3 x+1) y'(x)}{(x-1) (x+1)}-\frac {36 (x+1)^2 y(x)}{(x-1)^2 (3 x+5)^2} \] ✓ Mathematica : cpu = 0.0333284 (sec), leaf count = 72
DSolve[Derivative[2][y][x] == (-36*(1 + x)^2*y[x])/((-1 + x)^2*(5 + 3*x)^2) + ((1 + 3*x)*Derivative[1][y][x])/((-1 + x)*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (3 \log (1-x)+\log (3 x+5))}+\frac {1}{2} c_2 e^{\frac {1}{2} (3 \log (1-x)+\log (3 x+5))} (3 \log (1-x)+\log (3 x+5))\right \}\right \}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 34
dsolve(diff(diff(y(x),x),x) = 1/(x-1)*(3*x+1)/(1+x)*diff(y(x),x)-36*(1+x)^2/(x-1)^2/(3*x+5)^2*y(x),y(x))
\[y \left (x \right ) = \left (x -1\right )^{\frac {3}{2}} \sqrt {3 x +5}\, \left (3 c_{2} \ln \left (x -1\right )+c_{2} \ln \left (3 x +5\right )+c_{1}\right )\]