30.12.40 problem 46 (d)

Internal problem ID [7632]
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 : 46 (d)
Date solved : Tuesday, September 30, 2025 at 04:55:10 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+\operatorname {dif} \left (y, t\right )-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=-{\frac {17}{2}} \\ \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+dif(y(t),t)-6*y(t) = 0; 
ic:=[y(0) = 2, D(y)(0) = -17/2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 21

ode=D[y[t],{t,2}]+D[y[t],t]-6*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==-17/2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {17}{10} e^{-3 t} \left (e^{5 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) + 2*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): -17/2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {17 \sqrt {3} e^{\sqrt {3} t}}{12} + \frac {17 \sqrt {3} e^{- \sqrt {3} t}}{12} \]