a. Explanation Given Information: Differential equation d x d t + 7 x = 5 cos 2 t Initial condition is zero, x ( 0 ) = 0 Calculation: d x d t + 7 x = 5 cos 2 t The given differential equation is linear and nonhomogeneous, so the general solution will be the solution of homogeneous equation, d x d t + 7 x = 0 . d x d t + 7 x = 0 ⇒ x = A e − 7 t For a particular solution, x p = a cos 2 t + b sin 2 t ⇒ d x p d t = − 2 a sin 2 t + 2 b cos 2 t ⇒ d x p d t + 7 x p = − 2 a sin 2 t + 2 b cos 2 t + 7 ( a cos 2 t + b sin 2 t ) ⇒ d x p d t + 7 x p = ( 7 b − 2 a ) sin 2 t + ( 7 a + 2 b ) cos 2 t b. To determine Solution of given differential equation. c. To determine Solution of given differential equation.

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Author: Norman S. Nise

Publisher: WILEY

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The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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