Answer
$y=3x-1$
Work Step by Step
We are given that $ \dfrac{dy}{dx}=\dfrac{y+1}{x}$
We will separate the variables to obtain:
$\dfrac{dy}{y+1}=\dfrac{dx}{x}$
Integrate to obtain:
$\int \dfrac{dy}{y+1}=\int x \ dx$
This implies that $\ln |y+1|=\ln|x|+C$
After applying the initial conditions, $y=2$ when $x=1$, we get $C=\ln 3$
Therefore, we have: $\ln |y+1|=\ln|x|+ \ln 3 \implies e^{\ln |y+1|}=e^{\ln|x|+\ln (3)}$
or, $y=3x-1$
