67.11.5 problem 17.1 (e)

Internal problem ID [16606]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.1 (e)
Date solved : Thursday, October 02, 2025 at 01:36:55 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.035 (sec). Leaf size: 15

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

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