Get first order derivative from second order derivative
By Michael Henderson •
I am given:
$$ y'' = 11-y $$
$$y(2)=1 ; y'(2)=-4$$
and asked to use Euler's method to find $y(2.2)$ for $h=0.1$
To find $y'$ I simply took the integral of $y''$ to get:
$$y'=11x-yx$$
However, this does not satisfy the condition given above, that $y'(2)=-4$. Is this not the correct way of obtaining the first order derivative?
$\endgroup$ 11 Answer
$\begingroup$The first-order system for your second-order equation is simply\begin{align} y'&=v,\\ v'&=11-y, \end{align}and the first Euler step correspondingly\begin{align} y_1&=y_0+hv_0,\\ v_1&=v_0+h(11-y_0). \end{align}
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