76.15.6 problem 6

Internal problem ID [17647]
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 : 6
Date solved : Tuesday, January 28, 2025 at 10:47:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 21

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

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