ODE
\[ x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right ) \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.380306 (sec), leaf count = 75
\[\left \{\left \{y(x)\to -\frac {\sqrt {4 x^5+e^{5 c_1}}+e^{\frac {5 c_1}{2}}}{2 x^3}\right \},\left \{y(x)\to \frac {\sqrt {4 x^5+e^{5 c_1}}-e^{\frac {5 c_1}{2}}}{2 x^3}\right \}\right \}\]
Maple ✓
cpu = 0.456 (sec), leaf count = 45
\[\left [y \left (x \right ) = \frac {\textit {\_C1} -\sqrt {4 x^{5}+\textit {\_C1}^{2}}}{2 x^{3}}, y \left (x \right ) = \frac {\textit {\_C1} +\sqrt {4 x^{5}+\textit {\_C1}^{2}}}{2 x^{3}}\right ]\] Mathematica raw input
DSolve[x*(1 + x*y[x]^2)*y'[x] == y[x]*(2 - 3*x*y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> -1/2*(E^((5*C[1])/2) + Sqrt[E^(5*C[1]) + 4*x^5])/x^3}, {y[x] -> (-E^((5*C[1])/2) + Sqrt[E^(5*C[1]) + 4*x^5])/(2*x^3)}}
Maple raw input
dsolve(x*(1+x*y(x)^2)*diff(y(x),x) = (2-3*x*y(x)^2)*y(x), y(x))
Maple raw output
[y(x) = 1/2/x^3*(_C1-(4*x^5+_C1^2)^(1/2)), y(x) = 1/2/x^3*(_C1+(4*x^5+_C1^2)^(1/2))]