52.3.21 problem 23

Internal problem ID [8307]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL FUNCTIONS. EXERCISES 6.4. Page 267
Problem number : 23
Date solved : Wednesday, March 05, 2025 at 05:34:38 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

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

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

\[ y(x)\to c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.056 (sec). Leaf size: 12

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

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