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प्रश्न
The solution of the differential equation dy/dx = sec x – y tan x is:
(A) y sec x = tan x + c
(B) y sec x + tan x = c
(C) sec x = y tan x + c
(D) sec x + y tan x = c
उत्तर
(A)
`dy/dx+ytanx=secx`
The given equation is of the form
`dy/dx+Py=Q`
`I.f==e^(intPdx)=e^(inttanxdx)`
`=e^(log|secx|)`
=secx
Solution of the given equation is
`y.( I.F)=intQ(I.F)dx+c`
`ysecx=intsecxsecxdx+c`
ysecx=tanx+c
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