\[ y''(x)=-\frac {y'(x)}{x+1}-\frac {y(x)}{x (x+1)^2} \] ✓ Mathematica : cpu = 0.0176472 (sec), leaf count = 29
DSolve[Derivative[2][y][x] == -(y[x]/(x*(1 + x)^2)) - Derivative[1][y][x]/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 x}{x+1}+\frac {c_2 (x \log (x)-1)}{x+1}\right \}\right \}\] ✓ Maple : cpu = 0.019 (sec), leaf count = 22
dsolve(diff(diff(y(x),x),x) = -1/(1+x)*diff(y(x),x)-1/x/(1+x)^2*y(x),y(x))
\[y \left (x \right ) = \frac {\ln \left (x \right ) c_{2} x +c_{1} x -c_{2}}{1+x}\]