74.10.28 problem 28

Internal problem ID [16233]
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 : 28
Date solved : Tuesday, January 28, 2025 at 08:58:07 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 37

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

\[ y = \frac {\left (5+\sqrt {5}\right ) {\mathrm e}^{\frac {\left (\sqrt {5}-1\right ) t}{2}}}{10}-\frac {{\mathrm e}^{-\frac {\left (\sqrt {5}+1\right ) t}{2}} \left (-5+\sqrt {5}\right )}{10} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 49

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

\[ y(t)\to \frac {1}{10} e^{-\frac {1}{2} \left (1+\sqrt {5}\right ) t} \left (\left (5+\sqrt {5}\right ) e^{\sqrt {5} t}+5-\sqrt {5}\right ) \]