Internal problem ID [3089]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 341.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (a x +1\right ) y^{\prime }+a -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x*(a*x+1)*diff(y(x),x)+a-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\frac {a}{x}+c_{1}\right ) x}{a x +1} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 24
DSolve[x(1+a x)y'[x]+a-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a+c_1 x}{a x+1} \\ y(x)\to a \\ \end{align*}