64.4.3 problem 3

Internal problem ID [13292]
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 : 3
Date solved : Tuesday, January 28, 2025 at 05:16:10 AM
CAS classification : [_separable]

\begin{align*} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(2*r*(s(r)^2+1)+(r^4+1)*diff(s(r),r)=0,s(r), singsol=all)
 

\[ s \left (r \right ) = -\tan \left (\arctan \left (r^{2}\right )+2 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.373 (sec). Leaf size: 59

DSolve[2*r*(s[r]^2+1)+(r^4+1)*D[ s[r],r]==0,s[r],r,IncludeSingularSolutions -> True]
 

\begin{align*} s(r)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [\int _1^r-\frac {2 K[2]}{K[2]^4+1}dK[2]+c_1\right ] \\ s(r)\to -i \\ s(r)\to i \\ \end{align*}