Differential Equations/Equlibrium

[MAM]

I need help starting/working through the following problems:

a. Using the facts that P' = Q and Q' = P , along with the initial conditions P(0) = 1 and Q(0) = 0, find explicit formulas for P(t) and Q(t).

b. Use your part (a) solutions to verify that P'(t) = Q(t) and Q'(t) = P(t). Show your work.

c. Use your part (a) solutions to verify the identity (P(t))² - (Q(t))²​ = 1

 

[Deleted member 4993]

I need help starting/working through the following problems:

a. Using the facts that P' = Q and Q' = P , along with the initial conditions P(0) = 1 and Q(0) = 0, find explicit formulas for P(t) and Q(t).

b. Use your part (a) solutions to verify that P'(t) = Q(t) and Q'(t) = P(t). Show your work.

c. Use your part (a) solutions to verify the identity (P(t))² - (Q(t))²​ = 1

P'(t) = Q(t)

P"(t) = Q'(t) = P(t)

similarly:

Q"(t) = P'(t) = Q(t)


Now continue.....


Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.