(2y+xy)dx+2xdy=0

arenceabigns

arenceabigns

Answered

2020-12-16

(2y+xy)dx+2xdy=0

Answer & Explanation

coffentw

coffentw

Expert

2020-12-17Added 103 answers

Here the Differential equations is given by
(2y+xy)dx+2xdy=0.
This can be written as
y(2+x)dx+2xdy=02+xxdx+2ydy=0
(2x+1)dx+2ydy=0

d(2lnx+x)+d(2lny)=0

d(2lnx+x+2lny)=0

d(2lnx+x+2lny)=c

2lnx+x+2lny=c

lny=(c2lnxx)/2

y=ec2lnxx2
where cc is a arbitrary constants.

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