64.10.12 problem 12

Internal problem ID [13418]
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 : Tuesday, January 28, 2025 at 05:42:10 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(4*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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