Solve for the differential equations and get the general solution.

William Collins 2021-12-29 Answered
Solve for the differential equations and get the general solution. Simplify your answer free from In. dy=tanxtanydx
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Expert Answer

vrangett
Answered 2021-12-30 Author has 36 answers
dy=tanxtany dx
dytany=tanxdx
dysinycosy=tanxdx
cosy dysiny=tanx dx
cosysinydy=tanx dx
ln(siny)=ln(cosx)+C
eln(siny)=eln(cosx)+C
siny=eln(cosx)1eC
siny=(cosx)1.eC
siny=eCcosx
y=sin1(eCcosx)
Answer: The general solution is y=sin1(eCcosx)
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Hattie Schaeffer
Answered 2021-12-31 Author has 37 answers
Given differential equation
dy=tanxtany dx
dytany=tanx dx
cosysinydy=sinxcosxdx
Integrating, cosysinydy=sinxcosxdx (1)
We substitute left hand integral
u=siny
du=cosy dy
and right hand integral
cosx=v
sinx dx=dv
sinx dx=dv
Then from (1)
duu=dvv
ln(u)=ln(v)+ln(c)
ln(u)=ln(cv)
u=cv
vu=c
cosxsiny=c
Hence solution is cosxsiny=c
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karton
Answered 2022-01-09 Author has 439 answers

We know,
1)ln|a|+ln|b|=ln|ab|2)cotx dx=ln|sinx|+c1,c1 is an integration constant3)tanx dx=ln|cosx|+c2,c2 is an integration constant.Given differential equation,dy=tanxtany dx(1)dytany=tanx dxdytany=tanx dxcoty dy=tan x dxln|sinx|=ln|cosx|+ln(c),c is an integration constantln|sinx|+ln|cosx|=ln(c)ln|sinxcosx|=ln(c)sinxcosx=c is the required solution of (1).

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