The graph of the function `y=f(x)` passing through the point (0,1) and satisfying the differential equation `(dy)/(dx)+ycosx=cosx` is such that (a) it is a constant function. (b) it is periodic (c) it is neither an even nor an odd function. (d) it is continuous and differentiable for all `( e ) (f) xdot( g )` (h)

Options

A. It is constant function
B. It is periodic
C. it is neither an even nor an odd function.
D. it is continuous and differentiable for all x

Answer

A, B, D

Explanation

`(dy)/(dx)+ycosx=cosx` (linear)
I.F. =`e^(intcosxdx)=e^(sinx)`
Thus, solution is `ye^(sinx)=inte^(sinx)cosxdx=e^(sinx)+c`
When `x=0, y=1`, then c=0
Thus, y=1. Hence, option (1), (2), (4) are true.