differential equation, compute the time needed to repay the loan
You should not have the $A$ alone on the right. $y(0)=A$ is the initial condition, but the interest is applied to $y$. The differential equation comes from $\frac {dy}{dt}=$interest-payments, so $\frac {dy}{dt}=\frac {5\%}{12}y-900\left(\frac{1+t}{200}\right)=\frac y{240}-\frac 92(1+t)$.