Standard form for linear DEs

• $f$s and $g$ are all functions of the independent variable $t$
• all terms without the dependent variable are on the right side

All $f$ functions are constants $\to$ linear ODE with constant coefficients

• independent variable represents time $\to$ called time invariant DEs

If there are no terms on the right side ($g$s) the DE is said to be homogeneous

Otherwise, the DE is called nonhomogeneous

• $g(t)$ often will be called forcing term since it will often represent a force acting upon a system

$(t-4{)}^2{u}^{\prime }=2\sin (t)u$ is not in standard form

• $u^{\prime }-\frac{2\sin (t)}{(t-4{)}^2}u=0$ is in standard form