What are firstorder homogeneous and nonhomogeneous linear differential equations?
Differential Equations
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These differential equations may be longwinded phrases, but they are actually types of firstorder differential equations. A firstorder homogeneous linear differential equation can be written in the notation as follows:
The firstorder homogeneous linear differential equations are those that place all terms that include the unknown equation and its derivative on the lefthand side of the equation; on the righthand side, it is set equal to zero for all t.
The nonhomogeneous linear differential equations are those that, after isolating the linear terms containing y(t) and the partial differentials inside the above large parentheses on the left side of the equation, do not set the righthand side identically to zero. It is often represented by one function, such as the b(t) (see below). The standard notation is as follows: