Internal problem ID [11423]
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 1.4.1. Integrating factors. Exercises
page 41
Problem number: 3(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {R^{\prime }+\frac {R}{t}=\frac {2}{t^{2}+1}} \] With initial conditions \begin {align*} [R \left (1\right ) = 3 \ln \left (2\right )] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(R(t),t)+R(t)/t=2/(1+t^2),R(1) = 3*ln(2)],R(t), singsol=all)
\[ R \left (t \right ) = \frac {\ln \left (t^{2}+1\right )+2 \ln \left (2\right )}{t} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 17
DSolve[{R'[t]+R[t]/t==2/(1+t^2),{R[1]==Log[8]}},R[t],t,IncludeSingularSolutions -> True]
\[ R(t)\to \frac {\log \left (4 t^2+4\right )}{t} \]