Find y(0.2) for `y'=-y`, `x_0=0, y_0=1`, with step length 0.1 using Euler method (first order differential equation)

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

Euler method

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for `n=0,x_0=0,y_0=1`

`y_1=y_0+hf(x_0,y_0)`

`=1+(0.1)f(0,1)`

`=1+(0.1)*(-1)`

`=1+(-0.1)`

`=0.9`

`x_1=x_0+h=0+0.1=0.1`

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for `n=1,x_1=0.1,y_1=0.9`

`y_2=y_1+hf(x_1,y_1)`

`=0.9+(0.1)f(0.1,0.9)`

`=0.9+(0.1)*(-0.9)`

`=0.9+(-0.09)`

`=0.81`

`x_2=x_1+h=0.1+0.1=0.2`

`:.y(0.2)=0.81`

`n`	`x_n`	`y_n`	`x_(n+1)`	`y_(n+1)`
0	0	1	0.1	0.9
1	0.1	0.9	0.2	0.81

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