87.12.26 problem 29

Internal problem ID [23474]
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 : 29
Date solved : Thursday, October 02, 2025 at 09:42:12 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime }+10 y^{\prime }+20 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=5*diff(diff(y(t),t),t)+10*diff(y(t),t)+20*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 34

ode=5*D[y[t],{t,2}]+10*D[y[t],t]+20*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(20*y(t) + 10*Derivative(y(t), t) + 5*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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