\[ y'(x)=\frac {(y(x)-x+\log (x+1))^2+x}{x+1} \] ✓ Mathematica : cpu = 0.194336 (sec), leaf count = 24
DSolve[Derivative[1][y][x] == (x + (-x + Log[1 + x] + y[x])^2)/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to x-\log (x+1)+\frac {1}{-\log (x+1)+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.054 (sec), leaf count = 36
dsolve(diff(y(x),x) = ((y(x)-x+ln(1+x))^2+x)/(1+x),y(x))
\[y \left (x \right ) = \frac {-\ln \left (1+x \right )^{2}+\left (x -c_{1}\right ) \ln \left (1+x \right )+c_{1} x -1}{\ln \left (1+x \right )+c_{1}}\]