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Solution of the differential equation ...

Solution of the differential equation
`cosxdy=y(sinx-y)dx, 0ltxlt(pi)/(2)`is

A

`tanx=(secx+c)y`

B

`secx=(tanx+c)y`

C

`ysec x=tanx+c`

D

`ytanx =secx+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`cosxdy=y(sinx-y)dx`
`rArr (dy)/(dx)=ytanx-y^(2)secx`
`rArr 1/y^(2)(dy)/(dx)-1/ytanx=-secx`
Let `1/y=t`
`therefore -1/y^(2)(dy)/(dx)=(dt)/(dx)`
`rArr -(dt)/(dx) -t tanx=-secx`
`rArr-(dt)/(dx)+(tanx)t=secx`
I.F. `=e^(int(tanxdx))=secx`
The solution is
t(I.F.) = `int(I.F.)secxdx`
`rArr 1/ysecx=tanx+c`
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