26.7.31 problem Exercise 20, problem 32, page 220

Internal problem ID [7081]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20, problem 32, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:13 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+4*y(x) = 0; 
ic:=[y(0) = 1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 16

ode=D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} (3 x+1) \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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