73.11.30 problem 17.5 (f)

Internal problem ID [15344]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.5 (f)
Date solved : Tuesday, January 28, 2025 at 07:53:16 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.014 (sec). Leaf size: 24

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

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