Question

Equation y''- y= 0 has a solution y= C₁e^t

Answer 1

Solution;

Here,we verify that the given differential equation has an explicit solution y=C₁e^t

We calculate the first and second derivative;

y'=C₁e^t

y"=C₁e^t

Now we can replace the values in the equation ;

y"-y=C₁e^t-C₁e^t=0