\[ y''(x)=\frac {y'(x)}{x+1}-\frac {(3 x+1) y(x)}{4 x^2 (x+1)} \] ✓ Mathematica : cpu = 0.0136427 (sec), leaf count = 26
DSolve[Derivative[2][y][x] == -1/4*((1 + 3*x)*y[x])/(x^2*(1 + x)) + Derivative[1][y][x]/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to c_1 \sqrt {x}+c_2 \sqrt {x} (x+\log (x))\right \}\right \}\] ✓ Maple : cpu = 0.02 (sec), leaf count = 17
dsolve(diff(diff(y(x),x),x) = 1/(1+x)*diff(y(x),x)-1/4*(3*x+1)/x^2/(1+x)*y(x),y(x))
\[y \left (x \right ) = \sqrt {x}\, \left (\ln \left (x \right ) c_{2}+c_{2} x +c_{1}\right )\]