ODE No. 425

\[ (x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0 \]

✓ Mathematica : cpu = 0.0067445 (sec), leaf count = 21

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

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

✓ Maple : cpu = 0.036 (sec), leaf count = 45

dsolve((1+x)*diff(y(x),x)^2-(y(x)+x)*diff(y(x),x)+y(x) = 0,y(x))

\[y \left (x \right ) = x +2-2 \sqrt {1+x}\]