Internal problem ID [10605]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve(v(u)^3+ (u^3-u*v(u)^2)*diff(v(u),u)=0,v(u), singsol=all)
\[ v \left (u \right ) = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-2 c_{1}}}{u^{2}}\right )}{2}-c_{1}} \]
✓ Solution by Mathematica
Time used: 5.391 (sec). Leaf size: 56
DSolve[v[u]^3+ (u^3-u*v[u]^2)*v'[u]==0,v[u],u,IncludeSingularSolutions -> True]
\begin{align*} v(u)\to -i u \sqrt {W\left (-\frac {e^{-2 c_1}}{u^2}\right )} \\ v(u)\to i u \sqrt {W\left (-\frac {e^{-2 c_1}}{u^2}\right )} \\ v(u)\to 0 \\ \end{align*}