65.6.12 problem 12.1 (xii)

Internal problem ID [13761]
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 (xii)
Date solved : Tuesday, January 28, 2025 at 06:02:13 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 )&=4\\ y^{\prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

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

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

\[ y = \frac {4 \left ({\mathrm e}^{3 t}+2\right ) {\mathrm e}^{-2 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

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

\[ y(t)\to \frac {4}{3} e^{-2 t} \left (e^{3 t}+2\right ) \]