74.18.25 problem 31

Internal problem ID [16582]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 09:11:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=3 \,{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+13*y(t)=3*exp(-2*t),y(t), singsol=all)
 

\[ y = \left (\sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} \right ) {\mathrm e}^{-2 t} {\mathrm e}^{5 t}+\frac {3 \,{\mathrm e}^{-2 t}}{29} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 39

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+13*y[t]==3*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3 e^{-2 t}}{29}+c_2 e^{3 t} \cos (2 t)+c_1 e^{3 t} \sin (2 t) \]