63.5.15 problem 3(c)

Internal problem ID [13089]
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)
Date solved : Tuesday, January 28, 2025 at 04:51:56 AM
CAS classification : [_linear]

\begin{align*} R^{\prime }+\frac {R}{t}&=\frac {2}{t^{2}+1} \end{align*}

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)
 

\[ R = \frac {\ln \left (t^{2}+1\right )+2 \ln \left (2\right )}{t} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 17

DSolve[{D[ R[t],t]+R[t]/t==2/(1+t^2),{R[1]==Log[8]}},R[t],t,IncludeSingularSolutions -> True]
 

\[ R(t)\to \frac {\log \left (4 t^2+4\right )}{t} \]