29.3.9 problem 63

Internal problem ID [4671]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 63
Date solved : Monday, January 27, 2025 at 09:30:56 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x y \left (3+y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (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: 0.247 (sec). Leaf size: 49

DSolve[D[y[x],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*}