Chapter 26, Problem 16P

Solve the following differential equation from $t=0\text{ to 1}$

$\frac{dy}{dt}-10y$

with the initial condition $y\left(0\right)=1$. Use the following techniques to obtain your solutions: (a) analytically, (b) the explicit Euler method, and (c) the implicit Euler method. For (b) and (c) use $h=0.1\text{ and }0.2$. Plot your results.