Give the correct answer and solve the given equation: displaystyle{x}{y}{left.{d}{x}right.}-{left({y}+{2}right)}{left.{d}{y}right.}={0}

a2linetagadaW 2020-12-05 Answered
Give the correct answer and solve the given equation:
xydx(y+2)dy=0
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Expert Answer

Ayesha Gomez
Answered 2020-12-06 Author has 104 answers

We have to find the solution for the given differential equation
xydx=(y+2)dy.
We can separate the variables.
So,
xydx=(y+2)dy
(y+2y)dy=xdx
Integrating both sides we get,
(y+2y)dyxdx
(1+2y)dy=xdx
dy+(2y)dy=xdx
dy+2dyy=xdx
y+2log(y)=x22+C, where C is a constant of integration.
Hence, the solution of the given differential equation is,
y+2log(y)=x22+C, C is a constant

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Jeffrey Jordon
Answered 2021-11-03 Author has 2313 answers

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