\[ (x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.0039268 (sec), leaf count = 21
DSolve[y[x] - (x + y[x])*Derivative[1][y][x] + (1 + x)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 x+\frac {c_1{}^2}{-1+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.251 (sec), leaf count = 45
dsolve((1+x)*diff(y(x),x)^2-(y(x)+x)*diff(y(x),x)+y(x) = 0,y(x))
\[y \left (x \right ) = x +2-2 \sqrt {1+x}\]