59.6.4 problem 12.1 (iv)

Internal problem ID [15034]
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 : Thursday, October 02, 2025 at 10:02:12 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*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)+diff(y(t),t)-6*y(t) = 0; 
ic:=[y(0) = -1, D(y)(0) = 8]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -2 \,{\mathrm e}^{-3 t}+{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

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

\begin{align*} y(t)&\to e^{-3 t} \left (e^{5 t}-2\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): 8} 
dsolve(ode,func=y(t),ics=ics)
 

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