74.10.24 problem 24

Internal problem ID [16229]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:57:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 11

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

\[ y = -4 \left (t -1\right ) {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 13

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

\[ y(t)\to -4 e^t (t-1) \]