Internal problem ID [3327]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x y \left (y+3\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x) = x*y(x)*(3+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3}{-1+3 \,{\mathrm e}^{-\frac {3 x^{2}}{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.227 (sec). Leaf size: 49
DSolve[y'[x]==x*y[x](3+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 e^{\frac {3 x^2}{2}+3 c_1}}{-1+e^{\frac {3 x^2}{2}+3 c_1}} y(x)\to -3 y(x)\to 0 \end{align*}