2.434   ODE No. 434

\[ x^2 y'(x)^2-x^2-2 x y(x) y'(x)=0 \] Mathematica : cpu = 0.0519371 (sec), leaf count = 53

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

\[\left \{\left \{y(x)\to \frac {1}{2} e^{-c_1} \left (-x^2+e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right )\right \}\right \}\] Maple : cpu = 0.004 (sec), leaf count = 7

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

\[y \left (x \right ) = x +c_{1}\]