2.408   ODE No. 408

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

✓ Mathematica : cpu = 0.338681 (sec), leaf count = 97

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

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

✓ Maple : cpu = 0.068 (sec), leaf count = 73

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

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