80.6.13 problem 10 (b)

Internal problem ID [18577]
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 (b)
Date solved : Tuesday, January 28, 2025 at 12:00:52 PM
CAS classification : [_separable]

\begin{align*} 1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve((1+v(u)^2)+(1+u^2)*v(u)*diff(v(u),u)=0,v(u), singsol=all)
 

\begin{align*} v &= \sqrt {{\mathrm e}^{-2 \arctan \left (u \right )} c_{1} -1} \\ v &= -\sqrt {{\mathrm e}^{-2 \arctan \left (u \right )} c_{1} -1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.538 (sec). Leaf size: 59

DSolve[(1+v[u]^2)+(1+u^2)*v[u]*D[v[u],u]==0,v[u],u,IncludeSingularSolutions -> True]
 

\begin{align*} v(u)\to -\sqrt {-1+e^{-2 \arctan (u)+2 c_1}} \\ v(u)\to \sqrt {-1+e^{-2 \arctan (u)+2 c_1}} \\ v(u)\to -i \\ v(u)\to i \\ \end{align*}