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)*Derivative[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))