Internal problem ID [4364]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(u(v)*(1-v)+v^2*(1-u(v))*diff(u(v),v)=0,u(v), singsol=all)
\[ u \left (v \right ) = {\mathrm e}^{\frac {\ln \left (v \right ) v -\operatorname {LambertW}\left (-v \,{\mathrm e}^{c_{1} +\frac {1}{v}}\right ) v +c_{1} v +1}{v}} \]
✓ Solution by Mathematica
Time used: 3.83 (sec). Leaf size: 26
DSolve[u[v]*(1-v)+v^2*(1-u[v])*u'[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*}