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M. EULER’S METHOD - There are many differential equations whose solutions cannot be written as exact algebraic equations. However, you can still solve particular equations as accurately as you want by numerical methods. - Euler’s method is a procedure that can be used to construct a numerical approximation to the solution of a first order differential equation such that the solution curve must satisfy the initial condition when x x0 and y y0 . - To help you use the method you need to understand where it comes from: Ex. 1) 1 x 1 and given that the solution curve passes through 2,3 , find 2 an approximate value for f x at x 2.1 . a) Given f ' x b) Find the f 3 SUMMARY: dy f x, y with initial value x0 , y0 on the solution curve, the successive dx approximations to the solution curve can be generated using the following recursive equation: Given 𝑥𝑛+1 = 𝑥𝑛 + ℎ 𝑦𝑛+1 = 𝑦𝑛 + ℎ𝑓(𝑥𝑛 , 𝑦𝑛 )