74.11.15 problem 27

Internal problem ID [16265]
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 : 27
Date solved : Tuesday, January 28, 2025 at 08:59:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=32 t \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)-2*diff(y(t),t)-8*y(t)=32*t,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-2 t} c_{2} +{\mathrm e}^{4 t} c_{1} -4 t +1 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[D[y[t],{t,2}]-2*D[y[t],t]-8*y[t]==32*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -4 t+c_1 e^{-2 t}+c_2 e^{4 t}+1 \]