Internal problem ID [2982]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 234.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +a \right ) y^{\prime }-y \left (1-a y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((a+x)*diff(y(x),x) = y(x)*(1-a*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {a +x}{a x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.584 (sec). Leaf size: 31
DSolve[(a+x) y'[x]==y[x](1-a y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{a+\frac {e^{c_1}}{a+x}} \\ y(x)\to 0 \\ y(x)\to \frac {1}{a} \\ \end{align*}