35.8.10 problem 10

Internal problem ID [6217]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 10
Date solved : Monday, January 27, 2025 at 01:48:17 PM
CAS classification : [_separable]

\begin{align*} u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 33

dsolve(u(v)*(1-v)+v^2*(1-u(v))*diff(u(v),v)=0,u(v), singsol=all)
 

\[ u = v \,{\mathrm e}^{\frac {-\operatorname {LambertW}\left (-v \,{\mathrm e}^{\frac {c_{1} v +1}{v}}\right ) v +c_{1} v +1}{v}} \]

✓ Solution by Mathematica

Time used: 3.662 (sec). Leaf size: 26

DSolve[u[v]*(1-v)+v^2*(1-u[v])*D[u[v],v]==0,u[v],v,IncludeSingularSolutions -> True]
 

\begin{align*} u(v)\to -W\left (v \left (-e^{\frac {1}{v}-c_1}\right )\right ) \\ u(v)\to 0 \\ \end{align*}