ODE
\[ y'(x)=x y(x) (y(x)+3) \] ODE Classification
[_separable]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.249806 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\frac {3 e^{\frac {3 x^2}{2}+3 c_1}}{-1+e^{\frac {3 x^2}{2}+3 c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {3}{-1+3 \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = 3/(-1+3*exp(-3/2*x^2)*_C1)]