Solve differential equation:
y'''+4y''-16y'-64y=0 y(0)=0, y'(0)=26, y''(0)=-16

 The required solution of the given differential equation is

Step-by-step explanation:  We are given to solve the following differential equation :

Let, be an auxiliary solution of equation (i).

Then,

Substituting these values in equation (i), we get

So, the general solution is given by

Then, we have

With the conditions given, we get

and

From equation (iii), we get

From equation (ii), we get

Therefore, the required solution of the given differential equation is