ODE
\[ (2 y(x)+x) y'(x)^3+3 (y(x)+x) y'(x)^2+(y(x)+2 x) y'(x)=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.172961 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \frac {1}{2} \left (-x-\sqrt {-3 x^2+4 e^{c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-x+\sqrt {-3 x^2+4 e^{c_1}}\right )\right \},\{y(x)\to c_1\},\{y(x)\to -x+c_1\}\right \}\]
Maple ✓
cpu = 1.086 (sec), leaf count = 65
\[\left [y \left (x \right ) = -x +\textit {\_C1}, y \left (x \right ) = \frac {-\frac {x \textit {\_C1}}{2}-\frac {\sqrt {-3 \textit {\_C1}^{2} x^{2}+4}}{2}}{\textit {\_C1}}, y \left (x \right ) = \frac {-\frac {x \textit {\_C1}}{2}+\frac {\sqrt {-3 \textit {\_C1}^{2} x^{2}+4}}{2}}{\textit {\_C1}}, y \left (x \right ) = \textit {\_C1}\right ]\] Mathematica raw input
DSolve[(2*x + y[x])*y'[x] + 3*(x + y[x])*y'[x]^2 + (x + 2*y[x])*y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-x - Sqrt[4*E^C[1] - 3*x^2])/2}, {y[x] -> (-x + Sqrt[4*E^C[1] - 3*x^2])/2}, {y[x] -> C[1]}, {y[x] -> -x + C[1]}}
Maple raw input
dsolve((x+2*y(x))*diff(y(x),x)^3+3*(x+y(x))*diff(y(x),x)^2+(2*x+y(x))*diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = -x+_C1, y(x) = (-1/2*x*_C1-1/2*(-3*_C1^2*x^2+4)^(1/2))/_C1, y(x) = (-1/2*x*_C1+1/2*(-3*_C1^2*x^2+4)^(1/2))/_C1, y(x) = _C1]