- #1
JFonseka
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Homework Statement
Solve dy/dx = exp(x-y) given that y = ln 2 at x = 0
Homework Equations
None.
The Attempt at a Solution
Firstly let's get the equation into a form so we can re-arrange the x's and y's, and then re-arrange.
dy/dx = exp(x)/exp(y)
exp(y)*dy = exp(x)*dx
Integrate:
exp(y) = exp(x) + C
Substitute:
exp(ln(2)) = exp(0) + C
2 = 1 + C, therefore C = 1
Hence, exp(y) = exp(x) + 1, and take log to get an equation in the form of y = ...
ln(exp(y)) = ln(exp(x)) + ln(1) =>
y = x
Doesn't really look right though, am I right or wrong?
Edit: Solved-> ln(exp(y)) = ln(exp(x) + 1)
=> y(x) = ln(exp(x) + 1)
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