Solve differential equation y′+ycos⁡x=sin⁡xcos⁡x

Haven

Haven

Answered

2021-02-03

Solve differential equation y+ycosx=sinxcosx

Answer & Explanation

hosentak

hosentak

Expert

2021-02-04Added 100 answers

y+P(x)y=Q(x)
I.F.=ep(x)dx
yI.F=(Q(x)I.F.)dx
y+ycosx=sinxcosx
P(x)=cosx
Q(x)=sinxcosx
I.F.=ecosxdx=esinx
yI.F.=(Q(x)I.F.)dx
yesinx=(sinxcosxesinx)dx
Let sinx=u
cosxdx=du
yesinx=ueudu
=ueueu+C
=sinxesinxesinx+C
yesinx=sinxesinxesinx+C
y=sinx1+Cesinx

Jeffrey Jordon

Jeffrey Jordon

Expert

2021-12-25Added 2575 answers

Answer is given below (on video)

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