Internal problem ID [14256]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y={\mathrm e}^{-t}} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([diff(y(t),t)+y(t)=exp(-t),y(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} \left (t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 14
DSolve[{y'[t]+y[t]==Exp[-t],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} (t-1) \]