Yes, "D" is the derivative operator. But it is common notation in linear differential equations with constant coefficients to write, say,
as
. As long as the coefficients are constant, the "
" can be treated like a polynomial (if the coefficients are not constant, you run into problems with commutativity).
Slapmaxwell1, that is not what I get. Differentiating the second equation,
. From the first equation,
so
. From the second equation, [tex]2x= (D- 9)y[tex] so [tex]-10x= (-5D+ 45)y. Then
. You appear to have dropped the "14y".
is not going to factor easily but the equation
can be solved by completing the square or the quadratic formula.