76.15.1 problem 1

Internal problem ID [17642]
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 : 1
Date solved : Tuesday, January 28, 2025 at 10:47:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

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

\[ y = c_{2} {\mathrm e}^{3 t}+{\mathrm e}^{-t} c_{1} -{\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 22

DSolve[D[y[t],{t,2}]-2*D[y[t],t]-3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (c_2 e^{4 t}+c_1\right ) \]