Internal problem ID [11429]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime }+\frac {{\mathrm e}^{-t} x}{t}=t} \] With initial conditions \begin {align*} [x \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 23
dsolve([diff(x(t),t)+exp(-t)/t*x(t)=t,x(1) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \left (\int _{1}^{t}\textit {\_z1} \,{\mathrm e}^{-\operatorname {Ei}_{1}\left (\textit {\_z1} \right )}d \textit {\_z1} \right ) {\mathrm e}^{\operatorname {Ei}_{1}\left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.169 (sec). Leaf size: 31
DSolve[{x'[t]+Exp[-t]/t*x[t]==t,{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-\operatorname {ExpIntegralEi}(-t)} \int _1^te^{\operatorname {ExpIntegralEi}(-K[1])} K[1]dK[1] \]