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Differential Equations

Differential Equations

The Scoop on Euler Exercises

Example 1

Let y be the solution to the differential equation

that passes through the point (0, 0). Use Euler's Method to estimate y(1) with step size Δ x = 0.25.

Example 2

The function y = f (x) is a solution to the differential equation

and f (0) = 5. Estimate y(1) using Euler's method with four steps.

Example 3

The function y = f(x) is a solution to the d.e. y ' = x + y.

Estimate f(2) using Euler's method with 4 steps given that

f(0) = 1.

Example 4

Let y = f (x) be the solution to the initial value problem

Use Euler's method to estimate f (4) using 5 steps.