Question

In each of problems 5 through 11, find the general solution of the given differential equation

Answer 1

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function $y(t)=e^t$  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

What is a function?

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

$y_1(t) = e^t$

Given differential equations are,

y''-y = 0

 So that,  

$y' (t) = e^t, y'' (t) = e^t$

Substitute values in the given differential equation.

$e^t -e^t=0$

                   

Therefore, the function $y(t)=e^t$  is the solution of the given differential equation.

Another function;

$y(t)=cosht$  

So that,  

$y"(t)=sinht\\\\y"(t)=cosht$

Hence, function y(t)=cosht is solution of given differential equation.

Learn more about function here:

brainly.com/question/2253924

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