2.421   ODE No. 421

\[ x y'(x)^2-2 y(x) y'(x)-x=0 \] Mathematica : cpu = 0.0515107 (sec), leaf count = 53

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

\[\left \{\left \{y(x)\to \frac {1}{2} e^{-c_1} \left (-x^2+e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right )\right \}\right \}\] Maple : cpu = 0.49 (sec), leaf count = 32

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

\[y \left (x \right ) = -i x\]