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 = 0.0197003 (sec), leaf count = 61
\[\left \{\left \{y(x)\to c_1+\frac {x}{2}\right \},\left \{y(x)\to \left (\frac {3 c_1}{2}-i x^{3/2}\right ){}^{2/3}\right \},\left \{y(x)\to \left (\frac {3 c_1}{2}+i x^{3/2}\right ){}^{2/3}\right \}\right \}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) ={\frac {x}{2}}+{\it \_C1},[x \left ( {\it \_T} \right ) ={{\it \_C1}\,{{\it \_T}}^{2} \left ( {{\it \_T}}^{2}-{\it \_T}+1 \right ) ^{-{\frac {2}{3}}} \left ( {\it \_T}+1 \right ) ^{-{\frac {2}{3}}}},y \left ( {\it \_T} \right ) =-{{\it \_C1} \left ( {{\it \_T}}^{2}-{\it \_T}+1 \right ) ^{-{\frac {2}{3}}} \left ( {\it \_T}+1 \right ) ^{-{\frac {2}{3}}}}] \right \} \] 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),'implicit')
Maple raw output
[x(_T) = 1/(_T^2-_T+1)^(2/3)/(_T+1)^(2/3)*_T^2*_C1, y(_T) = -1/(_T^2-_T+1)^(2/3)/(_T+1)^(2/3)*_C1], y(x) = 1/2*x+_C1