2.422   ODE No. 422

\[ x y'(x)^2-2 y(x) y'(x)+4 x=0 \]

✓ Mathematica : cpu = 0.114329 (sec), leaf count = 81

DSolve[4*x - 2*y[x]*Derivative[1][y][x] + x*Derivative[1][y][x]^2 == 0,y[x],x]
 

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

✓ Maple : cpu = 0.033 (sec), leaf count = 30

dsolve(x*diff(y(x),x)^2-2*y(x)*diff(y(x),x)+4*x = 0,y(x))
 

\[y \left (x \right ) = -2 x\]