63.5.18 problem 3(f)

Internal problem ID [13092]
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(f)
Date solved : Tuesday, January 28, 2025 at 04:52:02 AM
CAS classification : [_linear]

\begin{align*} R^{\prime }&=\frac {R}{t}+t \,{\mathrm e}^{-t} \end{align*}

With initial conditions

\begin{align*} R \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 16

dsolve([diff(R(t),t)=R(t)/t+t*exp(-t),R(1) = 1],R(t), singsol=all)
 

\[ R = \left (-{\mathrm e}^{-t}+1+{\mathrm e}^{-1}\right ) t \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 19

DSolve[{D[ R[t],t]==R[t]/t+t*Exp[-t],{R[1]==1}},R[t],t,IncludeSingularSolutions -> True]
 

\[ R(t)\to \left (-e^{-t}+1+\frac {1}{e}\right ) t \]