74.9.5 problem 13

Internal problem ID [16181]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 08:56:31 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)-diff(y(t),t)-2*y(t)=0,y(0) = -1, D(y)(0) = -5],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]-D[y[t],t]-2*y[t]==0,{y[0]==-1,Derivative[1][y][0] ==-5}},y[t],t,IncludeSingularSolutions -> True]
 

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