# Apply Euler's method with the step h = \frac{1}{2} to find an approximation of y(1), where y...

## Question:

Apply Euler's method with the step {eq}h = \frac{1}{2} {/eq} to find an approximation of y(1), where y is the solution of the initial value problem.

y' = 1 + y, y(0) = 0.

## 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_1 = y_0 + h \cdot y_0' {/eq}, where {eq}y_0 {/eq}, {eq}h {/eq}, and {eq}y_0' {/eq}, have to be given or determined in order to the determine the unknown {eq}y_1 {/eq} value.

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{eq}y' = 1+y, y(0) = 0, y(1) = ?, h = 0.5 {/eq}

To solve this by applying the Euler's method, the formula is needed. The formula for the Euler's...

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.