74.11.1 problem 13

Internal problem ID [16251]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 08:58:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=8 \,{\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(y(t),t$2)+y(t)=8*exp(2*t),y(t), singsol=all)
 

\[ y = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} +\frac {8 \,{\mathrm e}^{2 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 25

DSolve[D[y[t],{t,2}]+y[t]==8*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {8 e^{2 t}}{5}+c_1 \cos (t)+c_2 \sin (t) \]