Internal problem ID [11629]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.922 (sec). Leaf size: 28
dsolve((exp(v(u))+1)*cos(u) + exp(v(u))*(1+sin(u))*diff(v(u),u)=0,v(u), singsol=all)
\[ v \left (u \right ) = -\ln \left (-\frac {1+\sin \left (u \right )}{-1+\sin \left (u \right ) {\mathrm e}^{c_{1}}+{\mathrm e}^{c_{1}}}\right )-c_{1} \]
✓ Solution by Mathematica
Time used: 5.457 (sec). Leaf size: 37
DSolve[(Exp[v[u]]+1)*Cos[u] + Exp[v[u]]*(1+Sin[u])*v'[u]==0,v[u],u,IncludeSingularSolutions -> True]
\begin{align*} v(u)\to \log \left (-1+\frac {e^{c_1}}{\left (\sin \left (\frac {u}{2}\right )+\cos \left (\frac {u}{2}\right )\right )^2}\right ) v(u)\to i \pi \end{align*}