64.10.12 problem 12

Internal problem ID [13347]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 12
Date solved : Monday, March 31, 2025 at 07:52:04 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.051 (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)
 

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