30.12.13 problem 13

Internal problem ID [7605]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 04:54:50 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=-12 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 10

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)-8*y(t) = 0; 
ic:=[y(0) = 3, D(y)(0) = -12]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 3 \,{\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 12

ode=D[y[t],{t,2}]+2*D[y[t],t]-8*y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-12}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 3 e^{-4 t} \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-8*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): -12} 
dsolve(ode,func=y(t),ics=ics)
 

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