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Homework Statement
Show that the given equation is an implicit solution of the given differential equation:
Homework Equations
e(x - y) + e(y - x) (dy / dx) = 0
e2y + e2x = 1
The Attempt at a Solution
(e2y) = 1 - e2x
solve for dy/dx
dy/dx (e2y) = dy/dx (1 - e2x)
(2e2y)(dy / dx) = -2e2x
dy / dx = -e2x / e2y
Substitute: e(x - y) + { e(y - x) * [ -e2x / e2y ] } = 0
Now I am uncomfortable on my algebra here, and I try to muliply out the
(please do not laugh if I am wrong) :{ e(y - x) * [ -e2x / e2y ] }
e(x - y) -[/color] e(y - x + 2x - 2y) = 0
e(x - y) - e(x - y) = 0
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