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# Euler's Method

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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) =

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:08 pm ad1c9bdddf
https://brainmass.com/math/ordinary-differential-equations/eulers-method-165771

## SOLUTION This solution is FREE courtesy of BrainMass!

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)) = 1 + 0.1*f(0,1) = 1 + 0.1*3 = 1.3
y(0.2) = y(0.1) + hf(0.1,y(0.1)) = 1.3 + 0.1*f(0.1,1.3) = 1.3 + 0.1*4.29 = 1.729
y(0.3) = y(0.2) + h(f(0.2,y(0.2)) = 1.729 + 0.1*f(0.2,1.729) = 1.729 + 0.1*6.2244 = 2.3514
y(0.4) = y(0.3) + h(f(0.3,y(0.3)) = 2.3514 + 0.1*f(0.3,2.3514) = 2.3514 + 0.1*9.17046 = 3.2684
y(0.5) = y(0.4) + h(f(0.4,y(0.4)) = 3.2684 + 0.1*f(0.4, 3.2684) = 3.2684 + 0.1*13.727432 = 4.6411

Finally, y(0.5) = 4.6411

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:08 pm ad1c9bdddf>
https://brainmass.com/math/ordinary-differential-equations/eulers-method-165771