10.9.15 problem 15

Internal problem ID [1317]
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 : 15
Date solved : Tuesday, March 04, 2025 at 12:29:03 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-4 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 15

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

\[ y = -\frac {{\mathrm e}^{-\frac {3 t}{2}} \left (-2+5 t \right )}{2} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 21

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

\[ y(t)\to \frac {1}{2} e^{-3 t/2} (2-5 t) \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = \left (1 - \frac {5 t}{2}\right ) e^{- \frac {3 t}{2}} \]