##### 4.19.14 $$x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0$$

ODE
$x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0$ ODE Classiﬁcation

[_rational]

Book solution method
Change of variable

Mathematica
cpu = 47.5929 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 181.974 (sec), leaf count = 0 , could not solve

dsolve(x^2*diff(y(x),x)^2+x*(x^2+x*y(x)-2*y(x))*diff(y(x),x)+(1-x)*(x^2-y(x))*y(x) = 0, y(x))

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(x^2*diff(y(x),x)^2+x*(x^2+x*y(x)-2*y(x))*diff(y(x),x)+(1-x)*(x^2-y(x))*y(x) = 0, y(x))

Maple raw output

dsolve(x^2*diff(y(x),x)^2+x*(x^2+x*y(x)-2*y(x))*diff(y(x),x)+(1-x)*(x^2-y(x))*y(
x) = 0, y(x))