13.7.3 problem 3

Internal problem ID [2366]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2, linear equations with constant coefficients. Page 138
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 02:08:20 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=diff(diff(y(t),t),t)-3*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) t}{2}}+c_2 \,{\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) t}{2}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 35

ode=D[y[t],{t,2}]-3*D[y[t],t]+y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) t} \left (c_2 e^{\sqrt {5} t}+c_1\right ) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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