Solve differential equation \frac{dy}{dx}-(\cot x)y= \sin^3x

Aneeka Hunt 2021-01-16 Answered
Solve differential equation dydx(cotx)y=sin3x
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AGRFTr
Answered 2021-01-17 Author has 95 answers
dydx+P(n)y=Q(n)
I.F=ep(x)dx
=ecotxdx
=elnsinn
=eln1sinn
I.F.=1sinn
y(I.F.)=(I.F.)Q(x)
1sinxy={sin3x}{sinx}dn
ysinx=sin2ndx
ysinx=1cos2x2dx
ysinx=12dxcos2x2dx
ysinx=x2sin2n4+c
y=2sinxsinxsinxsin2x4+c
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Answered 2021-12-12 Author has 2262 answers
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Answered 2021-12-14 Author has 2262 answers

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As pointed out when rearranging from u x + u = 1 u to ( 1 1 / u u ) d u = ( 1 x ) d x, we implicitly assumed that u ± 1. Equation (1) does not hold for u = ± 1
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Solving equation (1) for u with u ± 1, we arrive at the same family of equations but with c 0. The fact that c can be zero comes from setting u = ± 1
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