Question

A second-order linear differential equation for y(t) is said to be homogeneous if... every term involve either y or its derivatives, every term involve either tor its derivatives. every term is nonconstant. all terms are either constants or continuous functions in t.

Answer 1

Answer: Hello!

A second order differential equation has the next shape:

$y''(t) + p(t)y'(t) + q(t)y(t) = g(t)$

where p(t), q(t) and g(t) are functions of t, that can be constant numbers for example.

And is called homogeneus when g(t) = 0, so you have:

$y''(t) + p(t)y'(t) + q(t)y(t) = 0$

Then a second order differential equation is homogeneus ef every term involve either y or the derivatives of y.