76.15.30 problem 31

Internal problem ID [17671]
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 : 31
Date solved : Tuesday, January 28, 2025 at 10:53:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 y&=2 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

dsolve(diff(y(t),t$2)-3*diff(y(t),t)-4*y(t)=2*exp(-t),y(t), singsol=all)
 

\[ y = \frac {\left (-2 t +5 c_{2} \right ) {\mathrm e}^{-t}}{5}+{\mathrm e}^{4 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 32

DSolve[D[y[t],{t,2}]-3*D[y[t],t]-4*y[t]==2*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{25} e^{-t} \left (-10 t+25 c_2 e^{5 t}-2+25 c_1\right ) \]