Suppose that (x) satisfies the following equation (an example of a differential equation): (a) Show that (x)

Question:

Suppose that ƒ(x) satisfies the following equation (an example of a differential equation):

f"(x) = -f(x)

(a) Show that ƒ(x)2  + ƒ'(x)= ƒ(0)+ ƒ'(0)for all x. Show that the function on the left has zero derivative.
(b) Verify that sin x and cos x satisfy Eq. (1), and deduce that sin2 x + cosx = 1.


Eq.(1)

f'(c) = f(b)-f(a) b-a

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

Question Posted: