# Euler's Method

Use Eulers method with step size 0.1 to estimate y(0.5),

where y(x) is the solution of the initial-value problem y ' = 3y + 3xy,

y(0) = 1. (Give the answer to four decimal places.)

y(0.5) =

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#### Solution Preview

Let f(x,y) = 3y + 3xy, then y' = f(x,y)

By Euler's method with step size 0.1, we have h = 0.1, then

y(0) = 1,

y(0.1) = y(0) + hf(0,y(0)) = ...

#### Solution Summary

Euler's method is employed. The initial-value problems for the estimate methods are determined.

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