29.12.22 problem 341

Internal problem ID [4941]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 341
Date solved : Monday, January 27, 2025 at 09:53:11 AM
CAS classification : [_separable]

\begin{align*} x \left (a x +1\right ) y^{\prime }+a -y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x*(a*x+1)*diff(y(x),x)+a-y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 24

DSolve[x(1+a x)D[y[x],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*}