The differential equations, find a particular solution satisfying the given condition: `cos((dy)/(dx))=a(a in R); y=1`

Explanation

Given, `cos((dy)/(dx))=aimplies (dy)/(dx)=cos^(-1)a`
`implies dy=(cos^(-1)a)dx`
`implies intdy=cos^(-1)aintdx`
`implies y=cos^(-1)a(x)+C`
`y=1` and `x=0` then `1=cos^(-1)(a)xx0+CimpliesC=1`
put `C=1` in equation `(1)`,
`y=cos^(-1)a+1implies (y-1)/(x)=cos^(-1)a`
implies cos((y-1)/(x))=a`
which is the required particular solution.