Internal problem ID [10967]
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(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y-{\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+y(t)=exp(-t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} \left (1+\frac {t^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 19
DSolve[{y''[t]+2*y'[t]+y[t]==Exp[-t],{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-t} \left (t^2+2\right ) \\ \end{align*}