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Question

The solution of dydx+1=ex+yis


A

e-(x+y)+x+c=0

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B

e-(x+y)x+c=0

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C

ex+y+x+c=0

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D

ex+yx+c=0

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Solution

The correct option is A

e-(x+y)+x+c=0


Explanation for the correct option

\Find the solution of the given differential equation

Given:dydx+1=ex+y ….. (i)

Let, x+y=Z

dydx+1=dZdx …… (ii)

Now, comparing (i) and (ii), we get,

dZdx=eZdx=e-ZdZ

On integrating both sides, we get

dx=e-ZdZx+c=-e-Zx+e-x+y+c=0

Hence, option (A) is the correct answer.


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