The solution of dydx+1=ex+yis
e-(x+y)+x+c=0
e-(x+y)–x+c=0
ex+y+x+c=0
ex+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=eZ⇒dx=e-ZdZ
On integrating both sides, we get
∫dx=∫e-ZdZ⇒x+c=-e-Z⇒x+e-x+y+c=0
Hence, option (A) is the correct answer.