67.2.23 problem Problem 3(a)

Internal problem ID [13901]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 3(a)
Date solved : Wednesday, March 05, 2025 at 10:21:47 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 26

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

\[ y = c_{1} {\mathrm e}^{\left (-2+\sqrt {3}\right ) x}+c_{2} {\mathrm e}^{-\left (2+\sqrt {3}\right ) x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 34

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

\[ y(x)\to e^{-\left (\left (2+\sqrt {3}\right ) x\right )} \left (c_2 e^{2 \sqrt {3} x}+c_1\right ) \]

✓ Sympy. Time used: 0.164 (sec). Leaf size: 26

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

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