72.16.19 problem 19

Internal problem ID [14915]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 07:20:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(t),t$2)+2*diff(y(t),t)+y(t)=exp(-t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} \left (c_{2} +c_{1} t +\frac {1}{2} t^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 27

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+y[t]==Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-t} \left (t^2+2 c_2 t+2 c_1\right ) \]