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Write the general solution of differenti...

Write the general solution of differential equation `(dy)/(dx)=e^(x+y)`

A

`e^(x)+e^(-y)=c`

B

`e^(-x)+e^(-y)=c`

C

`e^(x)+e^(y)=c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(dt)/(dx)=e^xe^y`
`rArr(dy)/(e^y) =e^xdx`
Integrating both sides
`rArr-e^(-y)+c=e^(x)`
`rArre^(x)+e^(-y)=c`
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