Internal problem ID [3269]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 525.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (y+a \right ) y^{\prime }-y \left (B x +A \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 46
dsolve(x*(a+y(x))*diff(y(x),x) = y(x)*(B*x+A),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {A \ln \relax (x )+B x -a \LambertW \left (\frac {x^{\frac {A}{a}} {\mathrm e}^{\frac {B x}{a}+\frac {c_{1}}{a}}}{a}\right )+c_{1}}{a}} \]
✓ Solution by Mathematica
Time used: 1.034 (sec). Leaf size: 36
DSolve[x(a+y[x])y'[x]==y[x](A+B x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a \text {ProductLog}\left (\frac {x^{\frac {A}{a}} e^{\frac {B x+c_1}{a}}}{a}\right ) \\ y(x)\to 0 \\ \end{align*}