Question

Find a general solution of y" + 4y = 0.

Answer 1

`y(x)=C_(1)cos2x+C_(2)sin(2x)`

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:

`y(x)=C_(1)cos2x+C_(2)sin(2x)`