87.12.25 problem 28

Internal problem ID [23473]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 28
Date solved : Thursday, October 02, 2025 at 09:42:12 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

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

\[ y = \left (c_1 \,{\mathrm e}^{t \sqrt {65}}+c_2 \right ) {\mathrm e}^{-\frac {\left (9+\sqrt {65}\right ) t}{2}} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 35

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

\begin{align*} y(t)&\to e^{-\frac {1}{2} \left (9+\sqrt {65}\right ) t} \left (c_2 e^{\sqrt {65} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.134 (sec). Leaf size: 29

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

\[ y{\left (t \right )} = C_{1} e^{\frac {t \left (-9 + \sqrt {65}\right )}{2}} + C_{2} e^{- \frac {t \left (\sqrt {65} + 9\right )}{2}} \]