69.1.10 problem 10

Internal problem ID [14163]
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
Date solved : Tuesday, January 28, 2025 at 06:18:24 AM
CAS classification : [_separable]

\begin{align*} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.072 (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: 0.144 (sec). Leaf size: 35

DSolve[(1+u)*v[u]+(1-v[u])*u*D[ v[u],u]==0,v[u],u,IncludeSingularSolutions -> True]
 

\begin{align*} v(u)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]}dK[1]\&\right ][u+\log (u)+c_1] \\ v(u)\to 0 \\ \end{align*}