Question

proof superposition with dervation and explains​

Answer 1

Answer:

Linear differential equations can always be written as:

Lu = f,

where L is a linear differential operator (example: 1st or 2nd derivative operator), u is the unknown function of interest, and f is some inhomogeneous term, which is a function of the time/space variables (for homogeneous equations, set f = 0).

By the definition of linear operator, for any two functions f, g and constants a, b, we have:

L(af + bg) = aL(f) + bL(g).

Thus, if u is a solution of the inhomogeneous equation, i.e. Lu = f, and if v is a solution of the homogeneous equation, i.e. Lv = 0, then we have:

L(u + v) = Lu + Lv = f + 0 = f.

We conclude that (u + v) is also a solution of the

Answer 2

Answer:

The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. Wikipedia