Formula

1. Euler Rule `y_1=y_0+hf(x_0,y_0)`

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Examples
1. Find y(0.2) for `y'=(x-y)/2`, `x_0=0, y_0=1`, with step length 0.1 using Euler method (1st order derivative)

Solution:
Given `y'=(x-y)/(2), y(0)=1, h=0.1, y(0.2)=?`

Euler method
`y_1=y_0+hf(x_0,y_0)=1+(0.1)f(0,1)=1+(0.1)*(-0.5)=1+(-0.05)=0.95`

`y_2=y_1+hf(x_1,y_1)=0.95+(0.1)f(0.1,0.95)=0.95+(0.1)*(-0.425)=0.95+(-0.0425)=0.9075`

`:.y(0.2)=0.9075`

`n`	`x_n`	`y_n`	`x_(n+1)`	`y_(n+1)`
0	0	1	0.1	0.95
1	0.1	0.95	0.2	0.9075

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