Internal problem ID [3770]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 518.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \left (1+y\right ) y^{\prime }-\left (1-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*(1+y(x))*diff(y(x),x)-(1-x)*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (\frac {{\mathrm e}^{-x} x}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 4.467 (sec). Leaf size: 21
DSolve[x(1+y[x])y'[x]-(1-x)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to W\left (x e^{-x+c_1}\right ) y(x)\to 0 \end{align*}