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Use Taylor’S Series Method to Find a Solution of D Y D X = 1 + Y 2 , Y ( 0 ) at X = 0.1 Taking H=0.1 Correct Upto 3 Decimal Places. - Applied Mathematics 2

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Sum

Use Taylor’s series method to find a solution of `(dy)/(dx) =1+y^2, y(0)=0` At x = 0.1 taking h=0.1 correct upto 3 decimal places.

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Solution

`(dy)/(dx) =1+y^2`  𝒙𝟎=𝟎, 𝒚𝟎=𝟎, h=0.1

`y'=1+y^2    y_0'=1`

`y''=2yy'`      `y_0''=0`

`y'''=2yy''+2y'.y'`     `y_0'''=2`

Taylor’s series is given by :

`y(0/1)=y_0+h.y_0'+h^2/(2!)y_0''+....`

`=0+0.1(1)+(0.1xx0.1)/2(0)+(0.1+0.1+0.1)/6(2)`

`y(0.1)=0.10033`

Concept: Taylor’S Series Method
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