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 = 0.251035 (sec), leaf count = 61
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{x} \left (i \cosh \left (3 \sqrt [3]{x}\right )+c_1 \sinh \left (3 \sqrt [3]{x}\right )\right )}{i \sinh \left (3 \sqrt [3]{x}\right )+c_1 \cosh \left (3 \sqrt [3]{x}\right )}\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 19
\[\left [y \left (x \right ) = i \tan \left (-3 i x^{\frac {1}{3}}+\textit {\_C1} \right ) x^{\frac {1}{3}}\right ]\] 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))
Maple raw output
[y(x) = I*tan(-3*I*x^(1/3)+_C1)*x^(1/3)]