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 = 0.0122077 (sec), leaf count = 71

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

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

\[ \left \{ -{x}^{3} \left (y \relax (x ) \right ) ^{2}-2\,{x}^{2}+3\,xy \relax (x ) +{\it \_C1}=0 \right \} \] 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] -> -(-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