# Math Help - differential equation

1. ## differential equation

2. Hi

You can use matrices.

If X is the vector (x,y) then the equation is
$\dot{X} = A X$

where A is the matrix with -1 and 6 in the first row, and -1 and 4 in the second row

This matrix is diagonalisable since its eigenvalues are 1 and 2
The diagonal matrix is D with 1 ; 0 in the first row and 0 ; 2 in the second row
Then you can find the matrix P such that $P^{-1}AP = D$

If $Y = P^{-1}X$
Then the initial equation becomes $\dot{Y}=DY$ which can be easily solved

Then you can find X by $X = PY$