ODE
\[ 6 x y(x)^2 y'(x)+2 y(x)^3+x=0 \] ODE Classification
[[_homogeneous, `class G`], _exact, _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.00777719 (sec), leaf count = 99
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{4 c_1-x^2}}{2^{2/3} \sqrt [3]{x}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{4 c_1-x^2}}{2^{2/3} \sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{4 c_1-x^2}}{2^{2/3} \sqrt [3]{x}}\right \}\right \}\]
Maple ✓
cpu = 0.004 (sec), leaf count = 17
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}+{\frac {x}{4}}-{\frac {{\it \_C1}}{x}}=0 \right \} \] Mathematica raw input
DSolve[x + 2*y[x]^3 + 6*x*y[x]^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-x^2 + 4*C[1])^(1/3)/(2^(2/3)*x^(1/3))}, {y[x] -> -(((-1)^(1/3)*(-x^2 + 4*C[1])^(1/3))/(2^(2/3)*x^(1/3)))}, {y[x] -> ((-1)^(2/3)*(-x^2 + 4*C[1])^(1/3))/(2^(2/3)*x^(1/3))}}
Maple raw input
dsolve(6*x*y(x)^2*diff(y(x),x)+x+2*y(x)^3 = 0, y(x),'implicit')
Maple raw output
y(x)^3+1/4*x-1/x*_C1 = 0