87.12.28 problem 31

Internal problem ID [23476]
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 : 31
Date solved : Thursday, October 02, 2025 at 09:42:13 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }+4 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=6*diff(diff(y(t),t),t)+4*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {t}{3}} \left (c_1 \sin \left (\frac {\sqrt {2}\, t}{6}\right )+c_2 \cos \left (\frac {\sqrt {2}\, t}{6}\right )\right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 42

ode=6*D[y[t],{t,2}]+4*D[y[t],t]+y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t/3} \left (c_2 \cos \left (\frac {t}{3 \sqrt {2}}\right )+c_1 \sin \left (\frac {t}{3 \sqrt {2}}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + 4*Derivative(y(t), t) + 6*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} \sin {\left (\frac {\sqrt {2} t}{6} \right )} + C_{2} \cos {\left (\frac {\sqrt {2} t}{6} \right )}\right ) e^{- \frac {t}{3}} \]