2.223   ODE No. 223

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

✓ Mathematica : cpu = 0.0250404 (sec), leaf count = 55

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

\[\left \{\left \{y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right )\right \}\right \}\]

✓ Maple : cpu = 0.204 (sec), leaf count = 51

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

\[y \left (x \right ) = \frac {x c_{1} -\sqrt {5 c_{1}^{2} x^{2}+4}}{2 c_{1}}\]