ODE No. 441

\[ x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0 \] Mathematica : cpu = 0.0917761 (sec), leaf count = 65

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

\[\left \{\left \{y(x)\to -e^{-c_1} x \left (-x+2 \sqrt {2} e^{\frac {c_1}{2}}\right )\right \},\left \{y(x)\to e^{\frac {c_1}{2}} x \left (-2 \sqrt {2}+e^{\frac {c_1}{2}} x\right )\right \}\right \}\] Maple : cpu = 1.404 (sec), leaf count = 137

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

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