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 = 0.0111069 (sec), leaf count = 94

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

Maple
cpu = 0.008 (sec), leaf count = 22

\[ \left \{ \left (y \relax (x ) \right ) ^{-3}+{\frac {-3\,x-2\,{\it \_C1}+\ln \relax (x ) }{2\,{x}^{2}}}=0 \right \} \] 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),'implicit')

Maple raw output

1/y(x)^3+1/2*(-3*x-2*_C1+ln(x))/x^2 = 0