Solve the Bernoulli Differential equations. xy′ - y = xy^5

Wotzdorfg 2021-02-11 Answered
Solve the Bernoulli Differential equations. xyy=xy5
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Expert Answer

avortarF
Answered 2021-02-12 Author has 113 answers

Here the given differential equation is
xyy=xy5
which also can be written as
yyx=y5.
Let v=y4then dvdx=4y5dydx.The above De reduces to
y54dvdxyx=y5
149dvdxy4x=1
dvdx+4vx=4
x4dvdx+4vx3=4x4
ddx(vx4)=4x4
vx4=4x4dx+c
vx4=4x55+c
v=4x5+cx4
y4=4x5+cx4
y=(4x5+cx4)4
where c is a arbitrary constant.

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