In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos 0, sin 0) form a circle with...

Extracted text: In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos 0, sin 0) form a circle with a unit radius, the points (cosh 0, sinh 0) form the right half of the unit hyperbola. For an angle 0 in the rectangular coordinate plane as measured counterclockwise from the positive x-axis, the hyperbolic sine, sinh 0, and hyperbolic cosine, cosh 0, functions are defined by the following expressions: -- e et + e sinh 0 = & cosh e = 2 where e is the Euler's number. Consider a given primitive that is composed of hyperbolic functions, y = f(x) y = C1 cosh 5x + C2 sinh 5x Utilize the definition of both the hyperbolic sine and cosine functions to find the differential equation of order two (2) that the given primitive satisfies.