14.11.5 problem 5

Internal problem ID [2598]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:02:14 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: 0.004 (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: 0.027 (sec). Leaf size: 27

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

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