Euler€™s method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for each initial-value problem and then construct tables similar to tables (a) and (b).

y' = 2xy, y(1) = 1; y(1.5)

(a)

(b)

Actual value Abs. error % Rel. error 0.0000 1.00 1.0000 1.0000 0.00 1.10 1.0200 1.0212 0.0012 0.12 0.24 1.20 1.0424 1.0450 0.0025 1.30 1.0675 1.0714 0.0040 0.37 1.40 1.1008 0.0055 1.0952 0.50 1.50 1.1259 1.1331 0.0073 0.64 Actual value Abs. error % Rel. error 1.00 1.0000 1.0000 0.0000 0.00 1.05 1.0100 1.0103 0.0003 0.03 1.10 1.0206 1.0212 0.0006 0.06 1.15 1.0318 1.0328 0.0009 0.09 1.20 1.0437 1.0450 0.0013 0.12 1.25 1.0562 1.0579 0.0016 0.16 1.30 1.0694 1.0714 0.0020 0.19 1.35 1.0833 1.0857 0.0024 0.22 1.40 1.0980 1.1008 0.0028 0.25 1.45 1.1133 1.1166 0.0032 0.29 1.50 1.1295 1.1331 0.0037 0.32