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Find the general solutions of the follow...

Find the general solutions of the following differential equations.
(i) `(dy)/(dx) = e^(x+y)` (ii) `(dy)/(dx) = e^(y-x)`
(iii) `(dy)/(dx) = (xy+y)/(yx+x)`
(iv) `y(1+x)dx+x(1+y)dy = 0`

Text Solution

Verified by Experts

The correct Answer is:
(i) `e^(x) + e^(-y) = c` (ii) `e^(-x) - e^(-y) = c`
(iii) `y = cos e^(x-y)` (iv) x+y+log(xy) = c
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