67.3.5 problem Problem 6

Internal problem ID [14023]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 6
Date solved : Tuesday, January 28, 2025 at 06:12:57 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 8.913 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)-diff(y(t),t)-6*y(t)=0,y(0) = 2, D(y)(0) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[{D[y[t],{t,2}]-D[y[t],t]-6*y[t]==0,{y[0]==2,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t}+e^{3 t} \]