ODE No. 396

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

✓ Mathematica : cpu = 0.0775955 (sec), leaf count = 29

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

\[\left \{\left \{y(x)\to \frac {1}{x-c_1}\right \},\left \{y(x)\to c_1 e^{\frac {x^2}{2}}\right \}\right \}\]

✓ Maple : cpu = 0.011 (sec), leaf count = 20

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

\[y \left (x \right ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1}\]