Question

Find general solution of differential equation $\frac{dy}{dx}+y=1(y\ne 1)$.

Answer 1

Comparing given differential equation with first order linear equation, $\frac{dy}{dx}+Py=Q$

$P=1$ and $Q=1$

So integrating factor, $I.F.=e^{\int 1dx}=e^x$

Hence solution is given by, $y\cdot I.F=\int q\cdot I.F.dx$

$\Rightarrow y{e}^x=\int e^{x}dx=e^x+C$

$\Rightarrow y=1+C{e}^{-x}$