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Q. The solution of the differential equation `dy/dx` = `e^(y + x) + e^(y - x)` is A)...
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You need to separate the variables, such that:
`(dy)/(dx) = e^(y+x) + e^(y-x)`
Factoring out e^y yields:
`(dy)/(dx) = e^y*(e^x + 1/e^x)`
You need to divide by `e^y` both sides, such that:
`(dy)/(e^y(dx)) = (e^x + 1/e^x)`
You need to multiply by dx both sides, such that:
`(dy)/(e^y) = (e^x + 1/e^x)dx`
Integrating both sides, yields:
`int e^(-y)dy = int (e^x + 1/e^x)dx`
Using the property of linearity of integral yields:
`int e^(-y)dy = int (e^x)dx + int(1/e^x)dx`
`-e^(-y) = e^x - e^(-x) + c`
Hence, evaluating the solution to the given differential equation, yields `-e^(-y) = e^x - e^(-x) + c` , hence, you need to select the option D) none of these.
Posted by sciencesolve on July 5, 2013 at 6:06 PM (Answer #1)
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