In each problem 7 through 14, verify that each given function is a solution of the differential equation. Y" - y = 0; y1(t) = et, y2(t) = cosh t.

Since L.H.S = R.H.S = 0, for both and , y₁ and y₂ both satisfy the equation y" - y = 0 and are thus solutions to the differential equation.

Step-by-step explanation:

To check whether the given functions are solutions the given differential equation, we differentiate the functions and then insert it into the given equation.

So y" - y = 0 and  

Substituting these values of y and y" into the left hand side of the equation, we have

y" - y  

Since L.H.S = R.H.S

So is a solution of the differential equation.

When

Substituting y and y" into the left hand side of the equation, we have

y" - y

Since L.H.S = R.H.S

So, is a solution of the differential equation.

the answer is two. hope this !