8.9.1 problem 1

Internal problem ID [845]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 11:53:36 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 22

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

\[ y(x)\to e^{-2 x} \left (c_1 e^{4 x}+c_2\right ) \]

✓ Sympy. Time used: 0.056 (sec). Leaf size: 15

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

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