Answer:
[tex]y(x)=C_{1}cos2x+C_{2}sin(2x)[/tex]
Step-by-step explanation:
It is a linear homogeneous differential equation with constant coefficients:
y" + 4y = 0
Its characteristic equation:
r^2+4=0
r1=2i
r2=-2i
We use these roots in order to find the general solution:
[tex]y(x)=C_{1}cos2x+C_{2}sin(2x)[/tex]
