Question

The solution of differential equation
(D2 + 4) y = 0 is​

Answer 1

The solution is y = A cos 2x + B sin 2x

Given :

The differential equation ( D² + 4 )y = 0

To find :

The solution of the equation

Solution :

Step 1 of 3 :

Write down the given differential equation

Here the given differential equation is

( D² + 4 )y = 0

Step 2 of 3 :

Find roots of auxiliary equation

$\sf Let \: \: y = {e}^{mx} \: be \: the \: trial \: solution$

Then the auxiliary equation is

m² + 4 = 0

⇒ m = - 2i , 2i

Step 3 of 3 :

Find the solution

Hence the required solution is

y = A cos 2x + B sin 2x

Where A & B are constants