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Question

Solve the following differential equation: (x+y+1)dydx=1.

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Solution

(x+y+1)dydx=1

dydx=1x+y+1
Put, u=x+y dudx=1+dydx

=1+1u+1=u+2u+1

(u+1u+2)du=dx

(11u+2)du=dx

(11u+2)du=dx

uln|u+2|+ln|C|=x

lnCu+2=xu

Cu+2=exu

u+2=Ceux

(x+y)+2=Ce(x+y)x

x=Ceyy2

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