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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 6, sin 0) form a circle with a unit radius, the points (cosh 0, sinh 6) 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-0 e +e-0 sinh 0 = & cosh 0 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.

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 6, sin 0) form a circle with a unit radius, the points (cosh 0, sinh 6) 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-0 e +e-0 sinh 0 = & cosh 0 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 82E
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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 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® - e-0 e° +e-0 sinh 0 = & cosh e 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.
Transcribed Image 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® - e-0 e° +e-0 sinh 0 = & cosh e 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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