(i) Solve the following initial value problem: % = tan(x)y + sin(x) and y(0) = 0. (ii) Solve the initial value problem in (i) numerically by the Euler's method with h = 0.02 in the interval [0, 0.1] and give the absolute errors. (ii) Now we have Y' = f(x, Y) = sin(x) + Ytan(x) and Y(0) = 0. The Euler's method reads: Yn+1 = yn + hfix. v) n= 0, 1,2,3, ...,. with yo = Yo = 0 and Xn = 0.02n for n = 0, 1, 2, 3, 4, 5. $408 Computational Methods and Differential Equations with Applications Tutorial 11 e Exercise on D.E. We have n Xn yn Yn Absolute Errors 0 0.00 0.000000000 0.000000000 0.000000000 0.02 0.000000000 0.000200013 0.000200013 0.04 0.000399973 0.000800214 0.000400240 0.06 0.001200080 0.001801082 0.000601002 0.08 0.002400802 0.003203425 0.000802623 0.10 0.004002946 0.005008377 0.001005431