ODE
\[ 2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.175323 (sec), leaf count = 61
\[\left \{\left \{y(x)\to \frac {x}{2}+c_1\right \},\left \{y(x)\to \left (\frac {3 c_1}{2}-i x^{3/2}\right ){}^{2/3}\right \},\left \{y(x)\to \left (i x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3}\right \}\right \}\]
Maple ✓
cpu = 0.158 (sec), leaf count = 109
\[\left [x +\frac {x \textit {\_C1}}{y \left (x \right ) \left (\frac {-\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}} \left (\frac {-x +\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}}} = 0, x +\frac {x \textit {\_C1}}{y \left (x \right ) \left (\frac {\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}} \left (\frac {-x -\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}}} = 0, y \left (x \right ) = \frac {x}{2}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[-x + 2*x*y'[x] - y[x]*y'[x]^2 + 2*y[x]*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> x/2 + C[1]}, {y[x] -> ((-I)*x^(3/2) + (3*C[1])/2)^(2/3)}, {y[x] -> (I*x^(3/2) + (3*C[1])/2)^(2/3)}}
Maple raw input
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))
Maple raw output
[x+1/y(x)*x/((-(-x*y(x))^(1/2)+y(x))/y(x))^(2/3)/((-x+(-x*y(x))^(1/2)+y(x))/y(x))^(2/3)*_C1 = 0, x+1/y(x)*x/(((-x*y(x))^(1/2)+y(x))/y(x))^(2/3)/((-x-(-x*y(x))^(1/2)+y(x))/y(x))^(2/3)*_C1 = 0, y(x) = 1/2*x+_C1]