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APM2616 Assignment 3 DUE 22 July 2024 $2.75   Add to cart
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APM2616 Assignment 3 DUE 22 July 2024
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  • Course
  • Computer Algebra
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  • University Of South Africa
  • Book
  • Computer Algebra

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  • June 27, 2024
  • 9
  • 2023/2024
  • Exam (elaborations)
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  • apm2616 assignment 3 due 22 july 2024

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APM2616
Assignment 3
Due date: Monday, 22 July 2024

, Question 1


(1.1)
[ y' - yx cos x = 0 ]
[ y'( pi) = 1 ]


This is a first-order linear differential equation. We can solve it using the integrating
factor method.


The standard form is:
[ y' + P(x)y = Q(x) ]


Here, ( P(x) = -x cos x ) and ( Q(x) = 0 ).


The integrating factor ( mu(x) ) is:
[ mu(x) = e^{ int P(x) dx} = e^{ int -x cos x , dx} ]


Let's compute the integral:
[ int -x cos x , dx ]


Using integration by parts:
[ u = x, , dv = - cos x , dx ]
[ du = dx, , v = sin x ]


[ int -x cos x , dx = -x sin x + int sin x , dx = -x sin x - cos x + C ]


Thus, the integrating factor is:
[ mu(x) = e^{- left(x sin x + cos x right)} ]


Multiplying both sides of the original equation by the integrating factor:
[ e^{- left(x sin x + cos x right)} y' - e^{- left(x sin x + cos x right)} yx cos x = 0 ]

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