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Thank you for taking my question. I could really use some help with this question, I need to solve the initial value problem:

dy/dx=3*sin(x) and y=2 when x=0

Thank you again for your assistance, Clark

y(x) is obtained by integrating

y'(x) = 3sin(x)

to get

y(x) = -3cos(x) + C

where C is the "constant of integration". Note that, when y(x) is differentiated, this constant goes away. But it comes back when you integrate.

So far, the constant C is arbitrary. In order to determine the specific value of C, additional information for the problem is required. In this case, the initial condition, y(0) = 2, provides the needed info. So

y(0) = -3cos(0) + C = 2

=> -3 + C = 2     <-- since cos(0) = 1

or

C = 5

and

y(x) = -3cos(x) + 5.
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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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