ODE
\[ (a+x) y'(x)+y'(x)^2-y(x)=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.141939 (sec), leaf count = 13
\[\{\{y(x)\to c_1 (a+x+c_1)\}\}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 32
\[\left [y \left (x \right ) = -\frac {1}{4} x^{2}-\frac {1}{2} a x -\frac {1}{4} a^{2}, y \left (x \right ) = \textit {\_C1}^{2}+\textit {\_C1} a +x \textit {\_C1}\right ]\] Mathematica raw input
DSolve[-y[x] + (a + x)*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(a + x + C[1])}}
Maple raw input
dsolve(diff(y(x),x)^2+(a+x)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = -1/4*x^2-1/2*a*x-1/4*a^2, y(x) = _C1^2+_C1*a+_C1*x]