4.5.49 \(3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)\)

ODE
\[ 3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x) \] ODE Classification

[_rational, _Riccati]

Book solution method
Riccati ODE, Special cases

Mathematica
cpu = 0.0118605 (sec), leaf count = 61

\[\left \{\left \{y(x)\to \frac {\sqrt [3]{x} \left (c_1 \sinh \left (3 \sqrt [3]{x}\right )+i \cosh \left (3 \sqrt [3]{x}\right )\right )}{c_1 \cosh \left (3 \sqrt [3]{x}\right )+i \sinh \left (3 \sqrt [3]{x}\right )}\right \}\right \}\]

Maple
cpu = 0.015 (sec), leaf count = 17

\[ \left \{ {\it \_C1}+{\it Artanh} \left ({y \relax (x ) {\frac {1}{\sqrt [3]{x}}}} \right ) -3\,\sqrt [3]{x}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (x^(1/3)*(I*Cosh[3*x^(1/3)] + C[1]*Sinh[3*x^(1/3)]))/(C[1]*Cosh[3*x^(1
/3)] + I*Sinh[3*x^(1/3)])}}

Maple raw input

dsolve(3*x*diff(y(x),x) = 3*x^(2/3)+(1-3*y(x))*y(x), y(x),'implicit')

Maple raw output

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