ODE
\[ 3 x y'(x)=y(x) \left (x y(x)^3+2\right ) \] ODE Classification
[[_homogeneous, `class G`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.230389 (sec), leaf count = 84
\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{-3} x^{2/3}}{\sqrt [3]{-x^3+3 c_1}}\right \},\left \{y(x)\to \frac {x^{2/3}}{\sqrt [3]{-\frac {x^3}{3}+c_1}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} x^{2/3}}{\sqrt [3]{-\frac {x^3}{3}+c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 178
\[\left [y \left (x \right ) = \frac {3^{\frac {1}{3}} \left (x^{2} \left (-x^{3}+3 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{-x^{3}+3 \textit {\_C1}}, y \left (x \right ) = -\frac {3^{\frac {1}{3}} \left (x^{2} \left (-x^{3}+3 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{2 \left (-x^{3}+3 \textit {\_C1} \right )}-\frac {i 3^{\frac {5}{6}} \left (x^{2} \left (-x^{3}+3 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{2 \left (-x^{3}+3 \textit {\_C1} \right )}, y \left (x \right ) = -\frac {3^{\frac {1}{3}} \left (x^{2} \left (-x^{3}+3 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{2 \left (-x^{3}+3 \textit {\_C1} \right )}+\frac {i 3^{\frac {5}{6}} \left (x^{2} \left (-x^{3}+3 \textit {\_C1} \right )^{2}\right )^{\frac {1}{3}}}{-2 x^{3}+6 \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[3*x*y'[x] == y[x]*(2 + x*y[x]^3),y[x],x]
Mathematica raw output
{{y[x] -> -(((-3)^(1/3)*x^(2/3))/(-x^3 + 3*C[1])^(1/3))}, {y[x] -> x^(2/3)/(-1/3*x^3 + C[1])^(1/3)}, {y[x] -> ((-1)^(2/3)*x^(2/3))/(-1/3*x^3 + C[1])^(1/3)}}
Maple raw input
dsolve(3*x*diff(y(x),x) = (2+x*y(x)^3)*y(x), y(x))
Maple raw output
[y(x) = 1/(-x^3+3*_C1)*3^(1/3)*(x^2*(-x^3+3*_C1)^2)^(1/3), y(x) = -1/2/(-x^3+3*_C1)*3^(1/3)*(x^2*(-x^3+3*_C1)^2)^(1/3)-1/2*I*3^(5/6)/(-x^3+3*_C1)*(x^2*(-x^3+3*_C1)^2)^(1/3), y(x) = -1/2/(-x^3+3*_C1)*3^(1/3)*(x^2*(-x^3+3*_C1)^2)^(1/3)+1/2*I*3^(5/6)/(-x^3+3*_C1)*(x^2*(-x^3+3*_C1)^2)^(1/3)]