74.11.35 problem 47

Internal problem ID [16285]
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 : 47
Date solved : Tuesday, January 28, 2025 at 09:00:28 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 16

dsolve([diff(y(t),t$2)-y(t)=4,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]-y[t]==4,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 e^{-t} \left (e^t-1\right )^2 \]