89.14.24 problem 24

Internal problem ID [24628]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 128
Problem number : 24
Date solved : Thursday, October 02, 2025 at 10:46:34 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (c_1 \sin \left (2 x \right )+c_2 \cos \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+2*D[y[x],{x,1}]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 19

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

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