ODE
\[ a+x y'(x)^2-y(x) y'(x)=0 \] ODE Classification
[[_homogeneous, `class G`], _rational, _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.158252 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {a}{c_1}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.078 (sec), leaf count = 33
\[\left [y \left (x \right ) = -2 \sqrt {a x}, y \left (x \right ) = 2 \sqrt {a x}, y \left (x \right ) = x \textit {\_C1} +\frac {a}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[a - y[x]*y'[x] + x*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> a/C[1] + x*C[1]}}
Maple raw input
dsolve(x*diff(y(x),x)^2-y(x)*diff(y(x),x)+a = 0, y(x))
Maple raw output
[y(x) = -2*(a*x)^(1/2), y(x) = 2*(a*x)^(1/2), y(x) = x*_C1+a/_C1]