Solve differential equation dy/dx-(cot x)y= sin^3x

glasskerfu 2020-11-30 Answered
Solve differential equation dy/dx(cotx)y=sin3x
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Expert Answer

SchepperJ
Answered 2020-12-01 Author has 96 answers

dy/dx+Py=Q
P=cotx, Q=sin3x
I.F.=e(Pdx)
=e(cotxdx)
=e(ln(sinx)1)=(sinx)1=cosec x
ye(Pdx)=Qe(Pdx)dx+C
y cosec x=sin3x cosec xdx+C
y cosec x=1/2(1cos2x)dx+C (:cos2x=12sin2x)
y cosec x=1/2x1/2(sin2x)/2+C
y=1/2xsinx1/4sinxsin2x+C

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Jeffrey Jordon
Answered 2021-10-21 Author has 2064 answers

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