2.421   ODE No. 421

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

✓ Mathematica : cpu = 0.0726636 (sec), leaf count = 123

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

\[\left \{\left \{y(x)\to -\frac {x \tanh (-\log (x)+c_1)}{\sqrt {1-\tanh ^2(-\log (x)+c_1)}}\right \},\left \{y(x)\to \frac {x \tanh (-\log (x)+c_1)}{\sqrt {1-\tanh ^2(-\log (x)+c_1)}}\right \},\left \{y(x)\to -\frac {x \tanh (\log (x)+c_1)}{\sqrt {1-\tanh ^2(\log (x)+c_1)}}\right \},\left \{y(x)\to \frac {x \tanh (\log (x)+c_1)}{\sqrt {1-\tanh ^2(\log (x)+c_1)}}\right \}\right \}\]

✓ Maple : cpu = 0.034 (sec), leaf count = 32

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

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