ODE No. 471

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

✓ Mathematica : cpu = 0.0155543 (sec), leaf count = 47

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

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

✓ Maple : cpu = 0.015 (sec), leaf count = 33

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

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