4.12.5 \(2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0\)

ODE
\[ 2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0 \] ODE Classification

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

Book solution method
Exact equation

Mathematica
cpu = 0.0102903 (sec), leaf count = 58

\[\left \{\left \{y(x)\to -\frac {\sqrt {x \left (c_1+4 x^5\right )}+2 x^3}{x}\right \},\left \{y(x)\to \frac {\sqrt {x \left (c_1+4 x^5\right )}-2 x^3}{x}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 28

\[ \left \{ \ln \relax (x ) -{\it \_C1}+{\frac {1}{5}\ln \left ({\frac {4\,{x}^{2}y \relax (x ) + \left (y \relax (x ) \right ) ^{2}}{{x}^{4}}} \right ) }=0 \right \} \] Mathematica raw input

DSolve[y[x]*(12*x^2 + y[x]) + 2*x*(2*x^2 + y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((2*x^3 + Sqrt[x*(4*x^5 + C[1])])/x)}, {y[x] -> (-2*x^3 + Sqrt[x*(4*x
^5 + C[1])])/x}}

Maple raw input

dsolve(2*x*(2*x^2+y(x))*diff(y(x),x)+(12*x^2+y(x))*y(x) = 0, y(x),'implicit')

Maple raw output

ln(x)-_C1+1/5*ln((4*x^2*y(x)+y(x)^2)/x^4) = 0