29.8.29 problem 234

Internal problem ID [4834]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 234
Date solved : Monday, January 27, 2025 at 09:41:53 AM
CAS classification : [_separable]

\begin{align*} \left (x +a \right ) y^{\prime }&=y \left (1-a y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve((a+x)*diff(y(x),x) = y(x)*(1-a*y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x +a}{a x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.721 (sec). Leaf size: 34

DSolve[(a+x) D[y[x],x]==y[x](1-a y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {a+x}{a^2+a x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to \frac {1}{a} \\ \end{align*}