diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md index 9512dabd3f893c552d139cf2f3ac60a0429506e5..3309480fad8c800ebd7c18f3388822094dc05d09 100644 --- a/src/8_differential_equations_2.md +++ b/src/8_differential_equations_2.md @@ -56,11 +56,11 @@ $$y_{1} = y, \ y_{2} = y', \ \cdots, \ y_{n} = y^{(n-1)}.$$ Then, the differential equation can be re-written as $$\begin{split} -y_1 ' = & y_2 \\ -y_2 ' = & y_3 \\ -\vdots & \\ -y_{n-1} ' = & y_{n} \\ -y_{n} ' = & - a_{0} y_{1} - a_{1} y_{2} - \cdots - a_{n-1} y_{n}. +y_1 ' & = & y_2 \\ +y_2 ' & = & y_3 \\ +& \vdots & \\ +y_{n-1} '& = & y_{n} \\ +y_{n} ' & = & - a_{0} y_{1} - a_{1} y_{2} - \cdots - a_{n-1} y_{n}. \end{split}$$ Notice that together these $n$ equations form a linear first order system, the