2.1668   ODE No. 1668

\[ x y''(x)+(y(x)-1) y'(x)=0 \]

✓ Mathematica : cpu = 0.0703509 (sec), leaf count = 60

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

\[\left \{\left \{y(x)\to 2+\sqrt {2} \sqrt {2+c_1} \tanh \left (\frac {1}{2} \left (\sqrt {2} \sqrt {2+c_1} \log (x)-2 \sqrt {2} \sqrt {2+c_1} c_2\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.138 (sec), leaf count = 24

dsolve(x*diff(diff(y(x),x),x)-(1-y(x))*diff(y(x),x)=0,y(x))
 

\[y \left (x \right ) = \frac {2 c_{1} +\tanh \left (\frac {\ln \left (x \right )-c_{2}}{2 c_{1}}\right )}{c_{1}}\]