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 = 26.573 (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 = 23.999 (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),'implicit')

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),'implicit')

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),'implicit')