Internal problem ID [10398]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {R^{\prime }-\frac {R}{t}-t \,{\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [R \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(R(t),t)=R(t)/t+t*exp(-t),R(1) = 1],R(t), singsol=all)
\[ R \left (t \right ) = \left (-{\mathrm e}^{-t}+1+{\mathrm e}^{-1}\right ) t \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 18
DSolve[{R'[t]==R[t]/t+t*Exp[-t],{R[1]==1}},R[t],t,IncludeSingularSolutions -> True]
\begin{align*} R(t)\to t \left (\sinh (t)-\cosh (t)+\frac {1}{e}+1\right ) \\ \end{align*}