64.4.10 problem 10

Internal problem ID [13299]
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
Date solved : Tuesday, January 28, 2025 at 05:16:31 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.099 (sec). Leaf size: 32

dsolve(v(u)^3+ (u^3-u*v(u)^2)*diff(v(u),u)=0,v(u), singsol=all)
 

\[ v \left (u \right ) = \frac {{\mathrm e}^{-c_{1}}}{\sqrt {-\frac {{\mathrm e}^{-2 c_{1}}}{u^{2} \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-2 c_{1}}}{u^{2}}\right )}}} \]

✓ Solution by Mathematica

Time used: 1.928 (sec). Leaf size: 56

DSolve[v[u]^3+ (u^3-u*v[u]^2)*D[ v[u],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*}