Internal problem ID [3304]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 560.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (a +b y\right ) y^{\prime }-c y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 42
dsolve(x*(a+b*y(x))*diff(y(x),x) = c*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {a \LambertW \left (\frac {b \,x^{\frac {c}{a}} {\mathrm e}^{\frac {c c_{1}}{a}}}{a}\right )-c \ln \relax (x )-c c_{1}}{a}} \]
✓ Solution by Mathematica
Time used: 0.886 (sec). Leaf size: 36
DSolve[x(a+b y[x])y'[x]==c y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a \text {ProductLog}\left (\frac {b e^{\frac {c_1}{a}} x^{\frac {c}{a}}}{a}\right )}{b} \\ y(x)\to 0 \\ \end{align*}