Internal problem ID [10969]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 2(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {2 y^{\prime }+y-{\mathrm e}^{-\frac {t}{2}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([2*diff(y(t),t)+y(t)=exp(-t/2),y(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t -2\right ) {\mathrm e}^{-\frac {t}{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 19
DSolve[{2*y'[t]+y[t]==Exp[-t/2],{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-t/2} (t-2) \\ \end{align*}