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 = 0.320733 (sec), leaf count = 99
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}}\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 120
\[\left [y \left (x \right ) = \frac {\left (\left (-2 x^{2}+8 \textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{2 x}, y \left (x \right ) = -\frac {\left (\left (-2 x^{2}+8 \textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{4 x}-\frac {i \sqrt {3}\, \left (\left (-2 x^{2}+8 \textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{4 x}, y \left (x \right ) = -\frac {\left (\left (-2 x^{2}+8 \textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{4 x}+\frac {i \sqrt {3}\, \left (\left (-2 x^{2}+8 \textit {\_C1} \right ) x^{2}\right )^{\frac {1}{3}}}{4 x}\right ]\] 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))
Maple raw output
[y(x) = 1/2/x*((-2*x^2+8*_C1)*x^2)^(1/3), y(x) = -1/4/x*((-2*x^2+8*_C1)*x^2)^(1/3)-1/4*I*3^(1/2)/x*((-2*x^2+8*_C1)*x^2)^(1/3), y(x) = -1/4/x*((-2*x^2+8*_C1)*x^2)^(1/3)+1/4*I*3^(1/2)/x*((-2*x^2+8*_C1)*x^2)^(1/3)]