ODE No. 1768

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

✓ Mathematica : cpu = 0.0509715 (sec), leaf count = 53

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

\[\left \{\left \{y(x)\to -x-\sqrt {x^2+2 c_2 x^2+c_1}\right \},\left \{y(x)\to -x+\sqrt {x^2+2 c_2 x^2+c_1}\right \}\right \}\]

✓ Maple : cpu = 0.056 (sec), leaf count = 43

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

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