69.21.2 problem 697

Internal problem ID [18458]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 16. The method of isoclines for differential equations of the second order. Exercises page 158
Problem number : 697
Date solved : Thursday, October 02, 2025 at 03:12:19 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+6 x&=0 \end{align*}

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

ode:=diff(diff(x(t),t),t)+2*diff(x(t),t)+6*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{-t} \left (c_1 \sin \left (\sqrt {5}\, t \right )+c_2 \cos \left (\sqrt {5}\, t \right )\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 34

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

\begin{align*} x(t)&\to e^{-t} \left (c_2 \cos \left (\sqrt {5} t\right )+c_1 \sin \left (\sqrt {5} t\right )\right ) \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 26

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

\[ x{\left (t \right )} = \left (C_{1} \sin {\left (\sqrt {5} t \right )} + C_{2} \cos {\left (\sqrt {5} t \right )}\right ) e^{- t} \]