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 = 0.0229577 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \frac {1}{2} \left (-\sqrt {4 e^{c_1}-3 x^2}-x\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {4 e^{c_1}-3 x^2}-x\right )\right \},\left \{y(x)\to c_1\right \},\left \{y(x)\to c_1-x\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 42
\[ \left \{ -{\frac {1}{2}\ln \left ( {\frac {{x}^{2}+xy \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}} \right ) }-\ln \left ( x \right ) -{\it \_C1}=0,y \left ( x \right ) ={\it \_C1},y \left ( x \right ) =-x+{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = -x+_C1, -1/2*ln((x^2+x*y(x)+y(x)^2)/x^2)-ln(x)-_C1 = 0, y(x) = _C1