13.7.5 problem 5

Internal problem ID [2368]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2, linear equations with constant coefficients. Page 138
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:50:24 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-4 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: 0.014 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)-3*diff(y(t),t)-4*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {4 \,{\mathrm e}^{-t}}{5}+\frac {{\mathrm e}^{4 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 21

DSolve[{D[y[t],{t,2}]-3*D[y[t],t]-4*y[t]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{5} e^{-t} \left (e^{5 t}+4\right ) \]