(1 point) Euler's method for a first order IVP y' ` = f(x, y), y(xo) yo is the the following algorithm. From (xo, yo) we

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1 Point Euler S Method For A First Order Ivp Y F X Y Y Xo Yo Is The The Following Algorithm From Xo Yo We 1 (67.77 KiB) Viewed 23 times

(1 point) Euler's method for a first order IVP y' ` = f(x, y), y(xo) yo is the the following algorithm. From (xo, yo) we define a sequence of approximations to the solution of the differential equation so that at the nth stage, we have Χη = xn−1+h, Yn = Yn−1 + h • f(xn-1, Yn-1). In this exercise we consider the IVP y' = ey with y(0.5) = 2. This equation is first order with exact solution y = ln(e - e0.5 + e²). Use Euler's method with h = 0.4 to complete the following table: In the first two rows enter the values of an and yn and in the third row use the exact solution to find the errors en = ly(en) - Yn. A calculator or other scientific software would be handy to work these types of problem. You can always use answers given by explicit formulas which are very accurate. You need at least 4 significant digits. If your answer is marked wrong try entering a more accurate answer. 0 xn 0.5 n Yn 2 NO en 1 2 3 4