Question

# a)Program a calculator or computer to use Euler's method to compute y(1), where y(x) is the...

a)Program a calculator or computer to use Euler's method to compute y(1), where y(x) is the solution of the given initial-value problem. (Give all answers to four decimal places.)

 dy dx

+ 3x2y = 9x2,

y(0) = 4

 h = 1 y(1) = h = 0.1 y(1) = h = 0.01 y(1) = h = 0.001 y(1) =

(b) Verify that

y = 3 + ex3

is the exact solution of the differential equation.

y = 3 + ex3

⇒     y' =

LHS = y' + 3x2y =

+ 3x2(3 + ex3) = −3x2ex3 +

+ 3x2ex3 = 9x2 = RHS
y(0) =

+ e−0 = 3 + 1 = 4

(c) Find the errors in using Euler's method to compute y(1) with the step sizes in part (a). (Give all answers to four decimal places.)

 h = 1 error = (exact value − approximate value) = h = 0.1 error = (exact value − approximate value) = h = 0.01 error = (exact value − approximate value) = h = 0.001 error = (exact value − approximate value) =

What happens to the error when the step size is divided by 10?

When the step size is divided by 10, the error estimate is  ---Select--- divided by 5 multiplied by 10 divided by 10 multiplied by 5 divided by 100 (approximately).

Note: when h = 0.1, some part of calculation is

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