29.18.24 problem 500

Internal problem ID [5098]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 500
Date solved : Monday, January 27, 2025 at 10:11:07 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.064 (sec). Leaf size: 23

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

\[ x +\frac {b y \left (x \right )}{a +1}-y \left (x \right )^{-a} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 38

DSolve[(a x+b y[x])D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {\log \left (a+\frac {b y(x)}{x}+1\right )+a \log \left (\frac {y(x)}{x}\right )}{a+1}=-\log (x)+c_1,y(x)\right ] \]