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The Taylor's series expansion is

y = y_0+(x-x_0)y'_0+\frac{(x-x_0)^2}{2!}y''_0

Explanation

y = y_0-(x-x_0)y'_0-\frac{(x-x_0)^2}{2!}y''_0

Explanation

y = y_0+\frac{(x-x_0)^2}{2!}y''_0

Explanation

y = y_0+(x-x_0)y'_0-y''_0

Explanation

The error estimated in Taylor's series method
h = x - x_i 0 < θ < 1

E_n = \frac{h^{(n-1)}}{(n-1)!} f^{(n-1)} (\theta h)

Explanation

E_n = \frac{h^{(n+1)}}{(n)!} f^{(n+1)} (xi + h)

Explanation

E_n = \frac{h}{(n+1)!} f^{(n-1)} (xi + \theta h)

Explanation

E_n = \frac{h^{(n+1)}}{(n+1)!} f^{(n+1)} (xi + \theta h)

Explanation

ODE: Taylor's Series Method