What about source term in homogeneous linear differential equation?

Question

Can we say that a homogeneous linear differential equation has no source term?

Answer 1

In general, for an ODE of the form $L(u, du/dt, ...)=f(t)$ for the variable $u(t)$, the source term is the term on the right-hand-side of the equation, which depends only on the independent variable; in some cases it's also referred to as the forcing.

So to answer your question, if an ODE is homogeneous, then the source term is zero so yes we can think of the equation as having no source term. This rationale applies to general ODEs as well, not only linear ones.

Hope this helps!