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Consider inital value problem y'=2xy, y(0) = 1

Use Eulers Methos to estimate y(1) with 5 and 10 steps.

for 5 steps, increments are by 0.2

for 10 steps, increments are by 0.1

y_n+1 = y_n + h f(t_n , y_n)

where h is step size

the answer to the DE itself is y(x) = e^(x^2)

so these estimates should be close to e or 2.7182818...

i understand how to go from steps to step but i do not understand how to get the values for f(t_n , y_n)

all the examples ive looked at only had one variable so it is hard to compare

so for

y_1 = 1 + 0.2 f(t_1 , y_1)

y_2 = y_1 + 0.2 f(t_2 , y_2)

.

.

any help is appreciated

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# Eulers Method to Approximate Differential Eq.

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