30.12.17 problem 17

Internal problem ID [7609]
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 : 17
Date solved : Tuesday, September 30, 2025 at 04:54:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&={\frac {25}{3}} \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)-6*diff(y(t),t)+9*y(t) = 0; 
ic:=[y(0) = 2, D(y)(0) = 25/3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = {\mathrm e}^{3 t} \left (2+\frac {7 t}{3}\right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 19

ode=D[y[t],{t,2}]-6*D[y[t],t]+9*y[t]==0; 
ic={y[0]==2,Derivative[1][y][0] ==25/3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{3} e^{3 t} (7 t+6) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 25/3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\frac {7 t}{3} + 2\right ) e^{3 t} \]