Internal problem ID [12427]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (u +1\right ) v+\left (1-v\right ) u v^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((1+u)*v(u)+(1-v(u))*u*diff(v(u),u)=0,v(u), singsol=all)
\[ v \left (u \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-u}}{c_{1} u}\right ) \]
✓ Solution by Mathematica
Time used: 4.942 (sec). Leaf size: 28
DSolve[(1+u)*v[u]+(1-v[u])*u*v'[u]==0,v[u],u,IncludeSingularSolutions -> True]
\begin{align*} v(u)\to -W\left (-\frac {e^{-u-c_1}}{u}\right ) \\ v(u)\to 0 \\ \end{align*}