Question

Given following ODE's

1) x' = x / 1+t, with x(0) = 1 find x(2)

2) x' = t+x with x(0) = 1, find x(2)

3) x' = t-x, with x(1) =2 find x(3)

4) x' = t-x/t+x, with x(2) = 1, find x(4)

a) Solve each of the ODE's using Euler's method with h = 0.5, and calculate the relative error

i) x' = x/1+t: Approximation ____________________ Relative error: ________________

ii) x'= t+x; Approximation ____________________ Relative error: ________________

iii) x' = t-x; Approximation ____________________ Relative error: ________________

iv) x' = t-x/t+x; Approximation ____________________ Relative error: ________________

would you please sow me the steps?

Thank you.

Answer 1