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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

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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 @) form a circle with a unit radius, the points (cosh 0, sinh @) 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 - e-e e te-e sinh 0 = & cosh 0 = 2 2 where e is the Euler's number. Consider a given primitive that is composed of hyperbolic functions, y = f(x) y = C, sinh 2x + C2 cosh 2x 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

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