Mathematics - Differential Equation Question with Solution | TestHub

$\frac{dy}{dx}=\left(1+x\right)+\left(\frac{y-3}{1+x}\right)$

$\frac{dy}{dx}-\frac{1}{\left(1+x\right)}y=\left(1+x\right)-\frac{3}{(1+x)}$

I.F$=e^{-\int \frac{1}{(1+x)}dx}=\frac{1}{(1+x)}$

$\therefore \frac{d}{dx}\left(\frac{y}{1+x}\right)=x+3{\left(1+x\right)}^{-1}+c$

$\Rightarrow \frac{y}{1+x}=x+3{\left(1+x\right)}^{-1}+c$

$\Rightarrow y=\left(1+x\right)\left[x+\frac{3}{(1+x)}+c\right]$ , $\therefore$ at $x=2, y=0$

$\Rightarrow 0=3\left(2+1+c\right)$ $\Rightarrow c=-3$

At $x=3, y=3$