76.15.9 problem 9

Internal problem ID [17650]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 10:47:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\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)=3*exp(-t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} \left (c_{2} +c_{1} t +\frac {3}{2} t^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+y[t]==3*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-t} \left (3 t^2+2 c_2 t+2 c_1\right ) \]