2.388   ODE No. 388

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

✓ Mathematica : cpu = 0.563171 (sec), leaf count = 72

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

\[\text {Solve}\left [\left \{x=\frac {K[1] \tanh ^{-1}\left (\frac {K[1]}{\sqrt {K[1]^2+1}}\right )}{2 \sqrt {K[1]^2+1}}+\frac {c_1 K[1]}{\sqrt {K[1]^2+1}},y(x)=\frac {K[1]}{2}-\frac {x}{K[1]}\right \},\{y(x),K[1]\}\right ]\]

✓ Maple : cpu = 0.067 (sec), leaf count = 223

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

\[\frac {\frac {\left (y \left (x \right )-\sqrt {y \left (x \right )^{2}+2 x}\right ) \operatorname {arcsinh}\left (-y \left (x \right )+\sqrt {y \left (x \right )^{2}+2 x}\right )}{2}+x \sqrt {2 y \left (x \right )^{2}+2 x -2 y \left (x \right ) \sqrt {y \left (x \right )^{2}+2 x}+1}-2 c_{1} y \left (x \right )+2 c_{1} \sqrt {y \left (x \right )^{2}+2 x}}{\sqrt {2 y \left (x \right )^{2}+2 x -2 y \left (x \right ) \sqrt {y \left (x \right )^{2}+2 x}+1}} = 0\]