Internal problem ID [10388]
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: 2(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y-{\mathrm e}^{t}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(t),t)+y(t)=exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{t}}{2}+{\mathrm e}^{-t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 21
DSolve[y'[t]+y[t]==Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^t}{2}+c_1 e^{-t} \\ \end{align*}