76.15.3 problem 3

Internal problem ID [17644]
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 : 3
Date solved : Tuesday, January 28, 2025 at 10:47:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 29

dsolve(diff(y(t),t$2)-2*diff(y(t),t)-3*y(t)=-3*t*exp(-t),y(t), singsol=all)
 

\[ y = \frac {\left (6 t^{2}+16 c_{1} +3 t \right ) {\mathrm e}^{-t}}{16}+c_{2} {\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 37

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

\[ y(t)\to \frac {1}{64} e^{-t} \left (24 t^2+12 t+64 c_2 e^{4 t}+3+64 c_1\right ) \]