4.12.38 $x(3-2x^{2}y(x))y^{\prime }(x)=3x^{2}y(x{)}^2-3y(x)+4x$

ODE
$$x(3-2x^{2}y(x))y^{\prime }(x)=3x^{2}y(x{)}^2-3y(x)+4x$$ ODE Classification

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

Book solution method
Exact equation

Mathematica ✓
cpu = 0.0122077 (sec), leaf count = 71

$$\{\{y(x)\to -\frac{\sqrt{x^2(4c_{1}x-8x^3+9)}-3x}{2x^3}\},\{y(x)\to \frac{\sqrt{x^2(4c_{1}x-8x^3+9)}+3x}{2x^3}\}\}$$

Maple ✓
cpu = 0.013 (sec), leaf count = 24

$$\{-x^3{\left(y\left(x\right)\right)}^2-2x^2+3xy\left(x\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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] -> -(-3*x + Sqrt[x^2*(9 - 8*x^3 + 4*x*C[1])])/(2*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),'implicit')

Maple raw output

-x^3*y(x)^2-2*x^2+3*x*y(x)+_C1 = 0