The solution of differential equation dy dx + y = 1 is - Vidyadip

MCQ

The solution of differential equation $\frac{{dy}}{{dx}} + y = 1$ is

✓
$y = 1 + c\,{e^{ - x}}$
B
$y = 1 - c\,{e^{ - x}}$
C
$y = x + c\,{e^{ - x}}$
D
$y = x - c\,{e^{ - x}}$

✓

Answer

Correct option: A.

$y = 1 + c\,{e^{ - x}}$

a
(a) $\frac{{dy}}{{dx}} + y = 1$; $I.F. $$ = {e^{\int {Pdx} }} = {e^{\int {dx} }} = {e^x}$

Hence solution is $y.{e^x} = \int {{e^x}dx + c} $

$y{e^x} = {e^x} + c$ ==> $y = 1 + c{e^{ - x}}$.

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