ODE
\[ a+y(x)^2 y'(x)^2+2 x y(x) y'(x)-y(x)^2=0 \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.532531 (sec), leaf count = 41
\[\left \{\left \{y(x)\to -\sqrt {a+c_1 (-2 x+c_1)}\right \},\left \{y(x)\to \sqrt {a+c_1 (-2 x+c_1)}\right \}\right \}\]
Maple ✗
cpu = 0. (sec), leaf count = 0 , exception
time expired
Mathematica raw input
DSolve[a - y[x]^2 + 2*x*y[x]*y'[x] + y[x]^2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[a + C[1]*(-2*x + C[1])]}, {y[x] -> Sqrt[a + C[1]*(-2*x + C[1])]}}
Maple raw input
dsolve(y(x)^2*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a-y(x)^2 = 0, y(x))
Maple raw output
\verbtime expired||