Solve differential equation y'+2y=y^2

he298c 2020-11-02 Answered
Solve differential equationy+2y=y2
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Lacey-May Snyder
Answered 2020-11-03 Author has 88 answers

y+2y=y2
dy/dx=y22y
dy/dx=y(y2)
dy/(y(y2))=dx
Integrating both sides
dy/(y(y2))=dx
2/2dy/(y(y2))=dx
1/22/(y(y2))dy=dx
1/2(y(y2))/(y(y2))dy=dx(since yy+2=2)
Separating each parts
1/2(y/(y(y2))((y2))/(y(y2)))dy=dx
1/(y2)dy1/ydy=2dx
ln(y2)ln(y)=2x+C
ln((y2)/y)=2x+C
(y2)/y=e2x+C
=e2xeC
=e2xC
Where C is an arbitrary constant
(y2)/y=e2xC

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Jeffrey Jordon
Answered 2021-10-22 Author has 2047 answers

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