74.11.4 problem 16

Internal problem ID [16254]
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 : 16
Date solved : Tuesday, January 28, 2025 at 08:58:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 24

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

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