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Calculus: Early Transcendentals
(a) Program a calculator or computer to use Euler's method to compute $ y(1), $ where $ y(x) $ is the solution of the initial-value problem
$ \frac {dy}{dx} + 3x^2y = 6x^2 y(0) = 3 $
(i) $ h = 1 $ (ii) $ h = 0.1 $
(iii) $ h = 0.01 $ (iv) $ h = 0.001 $
(b) Verify that $ y = 2 + e^{-x^3} $ is the exact solution of the differential equation.
(c) Find the errors in using Euler's method to compute $ y(1) $ with the step sizes in part (a). What happens to the error when the step size is divided by 10?