72.13.2 problem 2

Internal problem ID [14784]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.6 page 342
Problem number : 2
Date solved : Thursday, March 13, 2025 at 04:18:54 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \left (c_{2} {\mathrm e}^{7 t}+c_{1} \right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 22

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

\[ y(t)\to e^{-3 t} \left (c_2 e^{7 t}+c_1\right ) \]

✓ Sympy. Time used: 0.145 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = C_{1} e^{- 3 t} + C_{2} e^{4 t} \]