The general solution solution of the ordinary differential equation d2y/dx2 +4y=0 ,where A & B are arbitrary constant is

The general solution of the given second order differential equation d²y/dx² + 4y = 0 is given by the formula:

y = Acos(2x) + Bsin(2x)

Here's the step by step solution:

1. The given differential equation is a second order homogeneous differential equation. The general form of such an equation is d²y/dx² + k²y = 0, where k is a constant.

2. The general solution of this type of equation is y = Acos(kx) + Bsin(kx), where A and B are arbitrary constants.

3. In the given equation, k² = 4, so k = 2.

4. Substituting k = 2 in the general solution, we get y = Acos(2x) + Bsin(2x).

So, the general solution of the given differential equation is y = Acos(2x) + Bsin(2x).