Question:

$In$ machine learning, certain algorithms, like gradient descent, can $be$ modeled using differential

equations $to$ track the change $in$ error over time. Consider the model:

$y^{\text{'}}=\frac{1+t}{1+y}$;$y(1)=2,in,1t2$

where $tis$ time $(in$ iterations$),$ and $y(t)$ represents the error $(loss)$ during training.

The actual solution $is$:

$y(t)=\sqrt[\phantom{2}]{t^2+2t+6}-1$

$a.$ Approximate $y(2)n=5n=5n=2t=2by$ comparing with the actual solution.

$c.$ Compare the methods and explain which method $is$ more accurate and why?