ODE
\[ -a x y'(x)+a y(x)+y'(x)^2=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.158852 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_1 \left (x-\frac {c_1}{a}\right )\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {a \,x^{2}}{4}, y \left (x \right ) = x \textit {\_C1} -\frac {\textit {\_C1}^{2}}{a}\right ]\] Mathematica raw input
DSolve[a*y[x] - a*x*y'[x] + y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*(x - C[1]/a)}}
Maple raw input
dsolve(diff(y(x),x)^2-a*x*diff(y(x),x)+a*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/4*a*x^2, y(x) = x*_C1-_C1^2/a]