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Differential Equations

Differential Equations

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

To get from 0 to 1 in four steps means

Here's the final table:

We conclude that

f (1) ≅ 4.9247

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.

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