65.6.4 problem 12.1 (iv)

Internal problem ID [13753]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (iv)
Date solved : Tuesday, January 28, 2025 at 06:01:54 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)+diff(y(t),t)-6*y(t)=0,y(0) = -1, D(y)(0) = 8],y(t), singsol=all)
 

\[ y = \left ({\mathrm e}^{5 t}-2\right ) {\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]+D[y[t],t]-6*y[t]==0,{y[0]==-1,Derivative[1][y][0] ==8}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (e^{5 t}-2\right ) \]