Euler\'s method for a first order IVP y,?f(x,y), y(x)-yo is the the following al

Question

Euler's method for a first order IVP y,?f(x,y), y(x)-yo is the the following algorithm. From (x0,y0) we define a sequence of approximations to the solution of the differential equation so that at the nth stage, we have In this exercise we consider the lVP y-1 + y2 with y(?0.5)-2. This equation is first order with exact solution y = tan(x + tan-1 (2)) Use Euler's method with h 0.5 to approximate the solution of the differential equation. Apply Euler's method to complete the following table: in the first two rows enter the values of x and y, and in the third row use the exact solution to find the errors ely(xy.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.

Explanation / Answer

Exact solution will be y(x)=tan(x+0.5+tan^-1(2))

n 0 1 2 3 4

x_n -0.5 0 0.5 1.0 1.5

y_n 2 4.5 15.125 130.0078 8581.5235

e_n 0 2.4556 13.0346 127.8696 8579.3358

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