Find the general solution of the differential equations `(dy)/(dx)+y=1(y!=1)`

Explanation

Given, `(dy)/(dx)+y=1implies(dy)/(dx)=1-y`
`implies dx=(dy)/(1-y)`
`implies int(dy)/((1-y))=intdx`
`implies -log|1-y|=x-Cimplies-x+C=log|1-y|`
`implies |1-y|=e^(-x+C)` (`:' log_(e)x=mimpliese^(m)=x`)
`implies y-1=(+-e^(C ))e^(-x)`
`implies y=1+Ae^(-x)` (where, `A=+-e^(C )`)