Consider a differential equation of the type dy dt f(t,y), (1) 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) = yo. 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) = y0), 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, 30). (b) Use the linear approximation to estimate the value of the solution at a nearby point, t₁ = to+h. We will denote your approximation by y₁. Provided that his sufficiently small, the line tangent and the solution will be close, and y₁ will be a reasonable approximation of the actual value of the solution, ults).