##### 4.20.37 $$\left (a^2-2 a x y(x)+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0$$

ODE
$\left (a^2-2 a x y(x)+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0$ ODE Classiﬁcation

[y=_G(x,y')]

Book solution method
No Missing Variables ODE, Solve for $$x$$

Mathematica
cpu = 25.2279 (sec), leaf count = 0 , could not solve

DSolve[y[x]^2 + 2*a*y[x]*Derivative[1][y][x] + (a^2 - 2*a*x*y[x] + y[x]^2)*Derivative[1][y][x]^2 == 0, y[x], x]

Maple
cpu = 20.931 (sec), leaf count = 0 , could not solve

dsolve((a^2-2*a*x*y(x)+y(x)^2)*diff(y(x),x)^2+2*a*y(x)*diff(y(x),x)+y(x)^2 = 0, y(x))

Mathematica raw input

DSolve[y[x]^2 + 2*a*y[x]*y'[x] + (a^2 - 2*a*x*y[x] + y[x]^2)*y'[x]^2 == 0,y[x],x]

Mathematica raw output

DSolve[y[x]^2 + 2*a*y[x]*Derivative[1][y][x] + (a^2 - 2*a*x*y[x] + y[x]^2)*Deriv
ative[1][y][x]^2 == 0, y[x], x]

Maple raw input

dsolve((a^2-2*a*x*y(x)+y(x)^2)*diff(y(x),x)^2+2*a*y(x)*diff(y(x),x)+y(x)^2 = 0, y(x))

Maple raw output

dsolve((a^2-2*a*x*y(x)+y(x)^2)*diff(y(x),x)^2+2*a*y(x)*diff(y(x),x)+y(x)^2 = 0,
y(x))