The correct solution of the differential equation (dy/dx) + y =1 where y≠1 is-
Answer & explanation
Correct answer: option 2
Given that differential equation
(dy/dx) + y =1
⇒ dy = (1-y) dx
separating the variables, we get:
dy/(1-y) = dx
now, integrating both sides we get:
∫dy/(1-y) =∫ dx
⇒ log(1-y) = x + log C
⇒ -log C - log(1-y) = x
⇒ log C(1-y) = -x
⇒ C(1-y)= e-x
y= 1 -(1/C) e-x