4.9.12 problem 12

Internal problem ID [1314]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 04:32:31 AM
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 )&=0 \\ y^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 10

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): 0, Subs(Derivative(y(t), t), t, 0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

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