Internal problem ID [11389]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises
page 26
Problem number: 4(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {R^{\prime }-\left (t +1\right ) \left (1+R^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(R(t),t)=(t+1)*(1+R(t)^2),R(t), singsol=all)
\[ R \left (t \right ) = \tan \left (\frac {1}{2} t^{2}+t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.315 (sec). Leaf size: 31
DSolve[R'[t]==(t+1)*(1+R[t]^2),R[t],t,IncludeSingularSolutions -> True]
\begin{align*} R(t)\to \tan \left (\frac {t^2}{2}+t+c_1\right ) R(t)\to -i R(t)\to i \end{align*}