Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

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A: Given,

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Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 4 and f(0) = 5. %3D %D Find f() =

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Q: 8. Show that the function y = ex (sin 2x + cos 2x) is a solution of the equation y" — 2y' + 5y = 0.

A: The given function is; y=ex(sin2x+cos2x) And the given equation is; y''-2y'+5y=0.

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Q: Find sin (x) if sec (x) sin (x) A = B = B = 26 24' where tan > 0. Put your answer in reduced form.

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Q: 음 (sin-" (2))\_-+ = (교2)) | dx 2(:) A 1+ 2() B (C 2 (4) cos-1 (16) D -2 (금) cot () csc(6) CSC

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Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: (b) y'= sin 4x.

A: The objective is to find y.

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

A: Solve the differential equation y"-2y'+y=5cos2x+10sin2x using the undetermined coefficients .

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

A: Integral problem

Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

A: