4.2.14 \(y'(x)=x y(x) (y(x)+3)\)

ODE
\[ y'(x)=x y(x) (y(x)+3) \] ODE Classification

[_separable]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0197666 (sec), leaf count = 39

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

Maple
cpu = 0.013 (sec), leaf count = 18

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}+{\frac {1}{3}}-{{\rm e}^{-{\frac {3\,{x}^{2}}{2}}}}{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x] == x*y[x]*(3 + y[x]),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(diff(y(x),x) = x*y(x)*(3+y(x)), y(x),'implicit')

Maple raw output

1/y(x)+1/3-exp(-3/2*x^2)*_C1 = 0