4.14.6 \(3 x y(x)^2 y'(x)=2 x-y(x)^3\)

ODE
\[ 3 x y(x)^2 y'(x)=2 x-y(x)^3 \] ODE Classification

[[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00758456 (sec), leaf count = 72

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

Maple
cpu = 0.006 (sec), leaf count = 17

\[ \left \{ -x-{\frac {{\it \_C1}}{x}}+ \left (y \relax (x ) \right ) ^{3}=0 \right \} \] Mathematica raw input

DSolve[3*x*y[x]^2*y'[x] == 2*x - y[x]^3,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(3*x*y(x)^2*diff(y(x),x) = 2*x-y(x)^3, y(x),'implicit')

Maple raw output

-x-1/x*_C1+y(x)^3 = 0