Find the solution of with y(0) 3 and y' (0) = 8. y = y" + 3y = 108 sin(3t) + 36 cos(3t)

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A: We have to solve

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A: Let's find.

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Q: 8. Differentiate with respect to x: (a) y = sin(x³), (b) y = sin³ x and (c) y = (7- cos(5x)) 2023

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Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

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Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

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Q: Find y'. sin t y = 8 + t %3D y' = %3D Find y'. 2 sin 0 + 9 cos 0 y = %3D sin 0 – cos 0 y' = %3D

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Q: Use the method of undetermined coefficients to solve y" – 2y' + y = 5 cos(2x) + 10 sin(2x)

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Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

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Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

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Q: /2 97. 3 sin x cos x =dx VI + 3 sin²x

A: Integral problem