Advertisements
Advertisements
प्रश्न
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.
योग
उत्तर
`(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`
shaalaa.com
Taylor’S Series Method
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
If 𝒚 satisfies the equation `(dy)/(dx)=x^2y-1` with `x_0=0, y_0=1` using Taylor’s Series Method find 𝒚 𝒂𝒕 𝒙= 𝟎.𝟏 (take h=0.1).
Use Taylor series method to find a solution of `dy/dx=xy+1,y(0)=0` X=0.2 taking h=0.1 correct upto 4 decimal places.
Expand 2 𝒙3 + 7 𝒙2 + 𝒙 – 6 in power of (𝒙 – 2) by using Taylors Theorem.
