\[ (a+x) y'(x)+y'(x)^2-y(x)=0 \] ✓ Mathematica : cpu = 0.0034375 (sec), leaf count = 18
DSolve[-y[x] + (a + x)*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to a c_1+c_1 x+c_1{}^2\right \}\right \}\] ✓ Maple : cpu = 0.025 (sec), leaf count = 20
dsolve(diff(y(x),x)^2+(x+a)*diff(y(x),x)-y(x) = 0,y(x))
\[y \left (x \right ) = -\frac {\left (x +a \right )^{2}}{4}\]