d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos 3x-2 sin 3x] 12 3

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A: This question can be solved by applying the concepts of integration of trigonometric functions.

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A: We can solve all the intregration problems with tha mathod of substitution. In substitution we use a…

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A: (b)

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A: Given, y=cos23x=cos3x2

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A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

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A: Given: y=2sin3x+π5-1

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A: Value of question (4) is 27ln(12)-21ln(4)-269 see below the calculation As per bartleby guideline I…

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A: We have given y=ln(sinx+5xe3xtan(x3)). Let us simplify right hand side using logarithmic…

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Q: :) 3 1 19. + dx x3 3x 20. | (2.x2 + x – 1)dx 2y4 + 1 / 2y4 Зуз 21. ip- 1 1 22. / (VE+1- + sin x – e"…

A: 19.  Let the given be I  I = ∫3x3 - 2x3 + 13xdx Now integrating given integral , we get  ⇒I = ∫3x-13…

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A: Note: As per our guidelines we are allowed to solve one question

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A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

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A: A

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A: Given: I=∫cos(4x)cos(3x)dx

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A: The given integral is: ∫x2cos 2x dx