# 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

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.

#### 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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