4.19.14 $x^2{y}^{\prime }(x{)}^2+x(x^2+xy(x)-2y(x))y^{\prime }(x)+(1-x)(x^2-y(x))y(x)=0$

ODE
$$x^2{y}^{\prime }(x{)}^2+x(x^2+xy(x)-2y(x))y^{\prime }(x)+(1-x)(x^2-y(x))y(x)=0$$ ODE Classification

[_rational]

Book solution method
Change of variable

Mathematica ✗
cpu = 49.8053 (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 = 259.019 (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),'implicit')

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),'implicit')

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),'implicit')