80.6.14 problem 10 (c)

Internal problem ID [18578]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 10 (c)
Date solved : Tuesday, January 28, 2025 at 12:00:55 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 10

dsolve(u*ln(u)*diff(v(u),u)+sin(v(u))^2=1,v(u), singsol=all)
 

\[ v = \arctan \left (\ln \left (\ln \left (u \right )\right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.359 (sec). Leaf size: 52

DSolve[u*Log[u]*D[v[u],u]+Sin[v[u]]==0,v[u],u,IncludeSingularSolutions -> True]
 

\begin{align*} v(u)\to -\arccos (-\tanh (-\log (\log (u))+c_1)) \\ v(u)\to \arccos (-\tanh (-\log (\log (u))+c_1)) \\ v(u)\to 0 \\ v(u)\to -\pi \\ v(u)\to \pi \\ \end{align*}