if the differential equation of a curve, passing through `(0,-(pi)/(4))` and `(t,0)` is `cosy((dy)/(dx)+e^(-x))+siny(e^(-x)-(dy)/(dx))=e^(e^(-x))` then find the value of `t.e^(e^(-1))`

Answer

1

Explanation

`(dy)/(dx)(cosy-siny)+(cosy+siny)e^(-x)=e^(e^(-x))`
`cosy+siny=u`
`implies(du)/(dx)+e^(-x)u=e^(e^(-x))=x`
`impliese^(-e^(-t))=timpliest.e^(e^(-t))=1`