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Question

Solve:-
(ex+1)ydy+(y+1)dx=0

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Solution

(ex+1)ydy+(y+1)dx=0

(ex+1)ydy=(y+1)dx

ydyy+1=dxex+1

(y+11)dyy+1=dxex(1+ex)

(y+1)dyy+1dyy+1=exdx(1+ex)

dydyy+1=exdx(1+ex)

Integrating both sides, we get

dydyy+1=exdx(1+ex)

Let t=1+exdt=exdx

ylog|y+1|=dtt

ylog|y+1|=log|t|

ylog|y+1|=log|1+ex|+c where t=1+ex
ylog|y+1|log|1+ex|c=0 is the required solution.


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