78.12.3 problem 1 (c)

Internal problem ID [18219]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 1 (c)
Date solved : Monday, March 31, 2025 at 05:23:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (2 \sqrt {2}\, x \right )+c_2 \cos \left (2 \sqrt {2}\, x \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 30

ode=D[y[x],{x,2}] +8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cos \left (2 \sqrt {2} x\right )+c_2 \sin \left (2 \sqrt {2} x\right ) \]

✓ Sympy. Time used: 0.057 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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