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.