The solution of the differential equation `(dy)/(dx)=secx-ytanx` is :

Options

A. `ysecx=tanx+c`
B. `ysecx+tanx=c`
C. `secx=ytanx+c`
D. `secx+ytanx=c`

Explanation

The given differential equation is ,
`(dy)/(dx)=secx-ytanx`
`therefore(dy)/(dx)+ytanx=secx`
This is the linear differential equation of the form
`(dy)/(dx)+P*y=Q`
where `P=tanxandQ =secx`
`thereforeI.F=eintp*dx=einttanx*dxelogsec(x|)=secx`
Now , `y*(I.F.)=int(I.F.)Q*dx`
`y*secx=intsec^(2)x*dx`
`y*secx=tanx+c`
Hence ,the correct answer from the given alternative is (a).