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))