13.9.2 problem 2

Internal problem ID [2388]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 2
Date solved : Sunday, March 30, 2025 at 12:00:03 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{\frac {3 t}{2}} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 20

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

\[ y(t)\to e^{3 t/2} (c_2 t+c_1) \]

✓ Sympy. Time used: 0.165 (sec). Leaf size: 14

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 = {} 
dsolve(ode,func=y(t),ics=ics)
 

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