Solve: `dy / dx + y secx = tanx`

Answer

` y*|secx+tanx|=secx +tanx-x+c`

Explanation

We are given

`dy / dx + y secx = tanx`


this is of the form `(dy)/(dx)+Py=Q`

here `P=secx` and `Q=tanx`


`therefore` I.F.`=e^(int Pdx)=e^(int secx dx)=e^(ln|secx+tanx|)=|secx+tanx|`


General Solution is

`y*(I.F.)=int Q*(I.F.)dx +c`


`rArr y*|secx+tanx|=int tanx*|secx+tanx|dx +c`


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