Chapter 10.7, Problem 16E

To determine

The greatest difference between the corresponding values in the second and third rows, where the differential equation $y\text{'}=2ty+e^{t^2}$, $y(0)=5$ has solution $y=\left(t+5\right)e^{t^2}$.

Fill the below table by finding the second row values using a numerical method and the third row values calculated from the solution.

$\begin{array}{cccccccccccc}{t}_i& 0& 0.2& 0.4& 0.6& 0.8& 1& 1.2& 1.4& 1.6& 1.8& 2\\ y_i& 5& & & & & & & & & & \\ y& 5& 5.412& & & & & & & & & 382.2\end{array}$