Use Euler's Method with three equal step sizes to estimate the value of y(0.3) for the differential equation y ' = x - y, with y(0) = 1.

Question

Use Euler's Method with three equal step sizes to estimate the value of y(0.3) for the differential equation y ' = x - y, with y(0) = 1.

Type your answer in the space below and give 3 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.482).

Answer 1

We have y(0) = 1; f(x,y) = x - y; h = 0.3/3 = 0.1;

y(0.1) = y(0) + h·f(0,1) = 1 + 0.1(0 - 1) = 0.9

y(0.2) = y(0.1) + hf(01,0.9) = 0.9 + 0.1(0.1 - 0.9 = 0.82

y(0.3) = 0.82 + hf(0.2,0.82) = 0.82 + 0.1(0.2 - 0.82) = 0.758