ODE No. 442

\[ x^2 y'(x)^2+(1-x) \left (y(x)^2-x^2 y(x)\right )+\left (x^3+x^2 y(x)-2 x y(x)\right ) y'(x)=0 \]

✓ Mathematica : cpu = 0.0358359 (sec), leaf count = 28

DSolve[(1 - x)*(-(x^2*y[x]) + y[x]^2) + (x^3 - 2*x*y[x] + x^2*y[x])*Derivative[1][y][x] + x^2*Derivative[1][y][x]^2 == 0,y[x],x]

\[\left \{\left \{y(x)\to c_1 e^{-x} x\right \},\left \{y(x)\to -x^2+c_1 x\right \}\right \}\]

✓ Maple : cpu = 0.017 (sec), leaf count = 21

dsolve(x^2*diff(y(x),x)^2+(x^2*y(x)-2*x*y(x)+x^3)*diff(y(x),x)+(y(x)^2-x^2*y(x))*(1-x) = 0,y(x))

\[y \left (x \right ) = \left (-x +c_{1} \right ) x\]