10.9.11 problem 11

Internal problem ID [1313]
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 : 11
Date solved : Tuesday, March 04, 2025 at 12:28:54 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 15

ode:=9*diff(diff(y(t),t),t)-12*diff(y(t),t)+4*y(t) = 0; 
ic:=y(0) = 2, D(y)(0) = -1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{\frac {2 t}{3}} \left (-6+7 t \right )}{3} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 15

ode=9*D[y[t],{t,2}]-12*D[y[t],t]+4*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -e^{2 t/3} t \]

✓ Sympy. Time used: 0.183 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 12*Derivative(y(t), t) + 9*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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