Question:

$\displaystyle \frac{dy}{dt} = \frac{t+y}{t+y+1}$ Solve for $\displaystyle y(t)=...$

Approach:

Letting $\displaystyle u=t+y+1$ then getting $\displaystyle \frac{dy}{dt} = \frac{du}{dt}-1$ and substituting into main equation to get $\displaystyle \frac{du}{dt}-1 = \frac{u-1}{u}$ and rearraning to get $\displaystyle \frac{du}{dt} + \frac{1}{u} = 2$ however it's not in integration factor form. How would I solve it?