##### 4.8.20 $$6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4$$

ODE
$6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4$ ODE Classiﬁcation

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.238002 (sec), leaf count = 94

$\left \{\left \{y(x)\to -\frac {\sqrt [3]{-2} x^{2/3}}{\sqrt [3]{3 x-\log (x)+2 c_1}}\right \},\left \{y(x)\to \frac {x^{2/3}}{\sqrt [3]{\frac {3 x}{2}-\frac {\log (x)}{2}+c_1}}\right \},\left \{y(x)\to \frac {(-1)^{2/3} x^{2/3}}{\sqrt [3]{\frac {3 x}{2}-\frac {\log (x)}{2}+c_1}}\right \}\right \}$

Maple
cpu = 0.03 (sec), leaf count = 174

$\left [y \left (x \right ) = \frac {\left (-2 x^{2} \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )^{2}\right )^{\frac {1}{3}}}{-2 \textit {\_C1} -3 x +\ln \left (x \right )}, y \left (x \right ) = -\frac {\left (-2 x^{2} \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )}-\frac {i \sqrt {3}\, \left (-2 x^{2} \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )}, y \left (x \right ) = -\frac {\left (-2 x^{2} \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )}+\frac {i \sqrt {3}\, \left (-2 x^{2} \left (-2 \textit {\_C1} -3 x +\ln \left (x \right )\right )^{2}\right )^{\frac {1}{3}}}{-4 \textit {\_C1} -6 x +2 \ln \left (x \right )}\right ]$ Mathematica raw input

DSolve[6*x^3*y'[x] == 4*x^2*y[x] + (1 - 3*x)*y[x]^4,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(6*x^3*diff(y(x),x) = 4*x^2*y(x)+(1-3*x)*y(x)^4, y(x))

Maple raw output

[y(x) = 1/(-2*_C1-3*x+ln(x))*(-2*x^2*(-2*_C1-3*x+ln(x))^2)^(1/3), y(x) = -1/2/(-
2*_C1-3*x+ln(x))*(-2*x^2*(-2*_C1-3*x+ln(x))^2)^(1/3)-1/2*I*3^(1/2)/(-2*_C1-3*x+l
n(x))*(-2*x^2*(-2*_C1-3*x+ln(x))^2)^(1/3), y(x) = -1/2/(-2*_C1-3*x+ln(x))*(-2*x^
2*(-2*_C1-3*x+ln(x))^2)^(1/3)+1/2*I*3^(1/2)/(-2*_C1-3*x+ln(x))*(-2*x^2*(-2*_C1-3
*x+ln(x))^2)^(1/3)]