##### 4.14.19 $$x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )$$

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))]