Answered: dx 44. - +8x = sin t. dt

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.10: Inverse Variation

Problem 5MRE

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obtain just a particular solution (the general solution can always
be obtained easily by adding an arbitrary multiple of a solution of the associated homogeneous equation). In these exercises, the forcing function is an elementary sinusoidal function. If the forcing function is cos 5t, then a particular solution of the form A cos 5t will not work. However, a linear combination of cos 5t and sin 5t will work. Thus, the form for xp is A cos 5t + B sin 5t, where the constants A and B are determined by substituting the assumed form of the particular solution into the differential equation for x.

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$C o n s i d e r t h e e q u a t i o n 44 \frac{d x}{d t} + 8 x = \sin t T o f i n d : t h e p a r t i c u l a r s o l u t i o n H e r e t h e f o r c i n g f u n c t i o n i s s i n t a n d a c c o r d i n g t o t h e a r g u m e n t g i v e n i n t h e q u e s t i o n, w e g e t t h a t P a r t i c u l a r s o l u t i o n x_{p} i s o f t h e f o r m A c o s t + B s i n t x_{p} = A c o s t + B s i n t$

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