Question
Download Solution PDFThe value of y at x = 0.1 to five places of decimals, by Taylor's series method, given that
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFHere, x0 = 0, y0 = 1, h = 0.1 so y(0, 1) = y1 = ?
Here, yI(x) = x2y - 1
⇒ yI(0) = -1
yII(x) = 2xy + x2yI
⇒ yII(0) = 0
yIII(x) = 2y + 2xyI + 2xyI + x2yII
⇒ yIII(0) = 2
yIV(x) = 2yI + 4(xyII + yI) + 2xyII + x2yIII
⇒ yIV(0) = -6 and so on......
Hence by Taylor series:
1 - 0.1 + 0 + 0.00033 + ......
= 0.90031 ≈ 0.90033
Last updated on Jul 2, 2025
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