89.33.12 problem 13

Internal problem ID [24996]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 17. Special Equations of order Two. Exercises at page 251
Problem number : 13
Date solved : Thursday, October 02, 2025 at 11:46:06 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\beta ^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+beta^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (\beta x \right )+c_2 \cos \left (\beta x \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to c_1 \cos (\beta x)+c_2 \sin (\beta x) \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 19

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

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