87.9.14 problem 29

Internal problem ID [23387]
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 74
Problem number : 29
Date solved : Thursday, October 02, 2025 at 09:40:56 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.035 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 5*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (\frac {2 \sqrt {5} x}{5} \right )} + C_{2} \cos {\left (\frac {2 \sqrt {5} x}{5} \right )} \]