The statement the rate of change of the rate of change of y equals y is a differential equation. True or False?

I think the question is saying that the second derivative of y is equal to y. It would not be a differential equation since differential equations are asking for the original function. The statement already provides the original function. But I'm not sure if my reasoning is correct.Thanks. Any help and advice would be appreciated.The statement the rate of change of the rate of change of y equals y is a differential equation. True or False?
This would be written as:





y'' - y = 0





This is most definitely a differential equation. It would be classified as a second-order, linear, homogeneous, ordinary differential equation with constant coefficents. The fact that is is a homogeneous equation with constant coefficents also implies that it is an autonomous equation;.





Solving a differential equation means finding an expression that defines the dependent variable (in this case, y) in terms of the independent variable (in this case, time). The original differential equation does *not* provide a definition of y in terms of t.





In this case, the general solution to the above differential equation is:





y(t) = A*exp(-t) + B*exp(+t)





where A and B are constants of integration that must be found from the initial conditions.