Formula Second Order Taylor Series Method y(x) = y(x;) + hy'(x;) + "(x,) When the Taylor's series is truncated after three terms, it is called second order Taylor's series method. Else, we write as...

By using
second order Taylor's series method formula solve the ordinary differentation equation.

Extracted text: Formula Second Order Taylor Series Method y(x) = y(x;) + hy'(x;) + "(x,) When the Taylor's series is truncated after three terms, it is called second order Taylor's series method. Else, we write as Vis = y; + hy + 2!


Extracted text: 5. Solve the following initial value problem (IVP) y' - xy = x; v(0) = 1 by using (c) third-order Taylor's series method with h = 0.2,0.25,0.5 and 0 sxsl. Hence, if the exact solution is y = 2eT -1, find its errors. ANSWER: (c) h= 0.2 kerrot| exact y. 1.000 1.000 1 0.2 1.040 1.040 0.000 0.4 1.166 1.167 0.001 3. 0.6 1.393 1.394 0.001 4 0.8 1.752 1.754 0.002 5 1.0 2.293 2.297 0.004 h = 0.25 Jerrot| exact 1.000 1.000 1 0.25 1.062 1.063 0.001 0.50 1.263 1.266 0.003 3 0.75 1.643 1.650 0.007 4 1.00 2.285 2.297 0.012 h = 0.5 kerrot| exact y. 1.000 1.000 1 0.5 1.250 1.266 0.016 1.0 2.241 2.297 0.056