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Consider the differential equation \frac{dy}{dx}=3x with initial condition y(0) = 3 . Use...

Question:

Consider the differential equation {eq}\frac{dy}{dx}=3x {/eq} with initial condition {eq}y(0) = 3 {/eq}.

Use Euler's method with two steps to estimate {eq}y(1) {/eq}

Euler's Method of Approximation:

Euler's method of approximation is used to estimate the values for solutions of differential equations at different points if it is difficult to do so algebraically. The formula to do this method is: {eq}y_{n+1} = y_{n} + h \cdot y_{n}' {/eq}, where {eq}y_{n} {/eq}, {eq}h {/eq}, and {eq}y_{n}' {/eq}, have to be given or determined in order to the determine the unknown {eq}y_{n+1} {/eq} value.

Answer and Explanation: 1

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{eq}\frac{dy}{dx} = 3x, y(0) = 3, y(1) = ?, h = \frac{1-0}{2} \Rightarrow h = 0.5 \text{ [(Estimated x value - Initial x value)/Steps to get to...

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Mathematical Models of Euler's Circuits & Euler's Paths

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Chapter 9 / Lesson 4
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The mathematical models of Euler circuits and Euler paths can be used to solve real-world problems. Learn about Euler paths and Euler circuits, then practice using them to solve three real-world practical problems.


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