Consider a differential equation of the type dy = f(t, y), (1) %3D dt where ƒ is a function that may depend on both t and y. We want to find the solution to this differential equation, y(t), with initial conditions prescribed by y(to) = y0- Our goal in this problem is to derive a computational scheme known as Euler's method, and see how it can be useful to approximate solutions to first-order differential equations. (a) From above, we are given an initial point in the solution (y(to) = yo), and an equation that describes the slope of the solution everywhere, Eq. 1. Use this information to find the linear approximation to the solution at the initial point (to, yo).

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