##### 4.12.38 $$x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x$$

ODE
$x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x$ ODE Classiﬁcation

[_exact, _rational, [_Abel, 2nd type, class B]]

Book solution method
Exact equation

Mathematica
cpu = 0.446296 (sec), leaf count = 71

$\left \{\left \{y(x)\to -\frac {-3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3}\right \},\left \{y(x)\to \frac {3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3}\right \}\right \}$

Maple
cpu = 0.021 (sec), leaf count = 47

$\left [y \left (x \right ) = \frac {3+\sqrt {-8 x^{3}+4 x \textit {\_C1} +9}}{2 x^{2}}, y \left (x \right ) = -\frac {-3+\sqrt {-8 x^{3}+4 x \textit {\_C1} +9}}{2 x^{2}}\right ]$ Mathematica raw input

DSolve[x*(3 - 2*x^2*y[x])*y'[x] == 4*x - 3*y[x] + 3*x^2*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -1/2*(-3*x + Sqrt[x^2*(9 - 8*x^3 + 4*x*C[1])])/x^3}, {y[x] -> (3*x + S
qrt[x^2*(9 - 8*x^3 + 4*x*C[1])])/(2*x^3)}}

Maple raw input

dsolve(x*(3-2*x^2*y(x))*diff(y(x),x) = 4*x-3*y(x)+3*x^2*y(x)^2, y(x))

Maple raw output

[y(x) = 1/2/x^2*(3+(-8*x^3+4*_C1*x+9)^(1/2)), y(x) = -1/2*(-3+(-8*x^3+4*_C1*x+9)
^(1/2))/x^2]