Internal problem ID [3246]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 500.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (a x +b y\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 23
dsolve((a*x+b*y(x))*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\[ x +\frac {b y \relax (x )}{a +1}-y \relax (x )^{-a} c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 38
DSolve[(a x+b y[x])y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\log \left (a+\frac {b y(x)}{x}+1\right )+a \log \left (\frac {y(x)}{x}\right )}{a+1}=-\log (x)+c_1,y(x)\right ] \]