Internal problem ID [13608]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(4*diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\frac {x}{2}\right )+c_{2} \cos \left (\frac {x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 24
DSolve[4*y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos \left (\frac {x}{2}\right )+c_2 \sin \left (\frac {x}{2}\right ) \]