Internal problem ID [10598]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.316 (sec). Leaf size: 31
DSolve[2*r*(s[r]^2+1)+(r^4+1)*s'[r]==0,s[r],r,IncludeSingularSolutions -> True]
\begin{align*} s(r)\to -\tan \left (\arctan \left (r^2\right )-c_1\right ) \\ s(r)\to -i \\ s(r)\to i \\ \end{align*}