87.12.5 problem 5

Internal problem ID [23453]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:41:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (\sqrt {6}\, x \right )+c_2 \cos \left (\sqrt {6}\, x \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 28

ode=D[y[x],{x,2}]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \cos \left (\sqrt {6} x\right )+c_2 \sin \left (\sqrt {6} x\right ) \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (\sqrt {6} x \right )} + C_{2} \cos {\left (\sqrt {6} x \right )} \]