2.540   ODE No. 540

\[ 2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0 \]

✓ Mathematica : cpu = 0.0273933 (sec), leaf count = 69

DSolve[-x + 2*x*Derivative[1][y][x] - y[x]*Derivative[1][y][x]^2 + 2*y[x]*Derivative[1][y][x]^3 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {x}{2}+c_1\right \},\left \{y(x)\to \frac {\left (3 c_1-2 i x^{3/2}\right ){}^{2/3}}{2^{2/3}}\right \},\left \{y(x)\to \frac {\left (2 i x^{3/2}+3 c_1\right ){}^{2/3}}{2^{2/3}}\right \}\right \}\]

✓ Maple : cpu = 0.087 (sec), leaf count = 109

dsolve(2*y(x)*diff(y(x),x)^3-y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-x=0,y(x))
 

\[x +\frac {x c_{1}}{\left (\frac {-\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{{2}/{3}} \left (\frac {-x +\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{{2}/{3}} y \left (x \right )} = 0\]