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Question:

what is the use of second order differential equation with variable coefficients?

what is the use of second order differential equation with variable coefficients?

Answer:

The easiest one I can think of is acceleration, second order derivative of position. Second order derivatives have a wide variety of uses where something is being affected by time, such as population growth as well.
These sort of differential equations occur in the design of suspension systems for cars or aircraft. I have even seen them used in the design of a suspension system for railway track underground to minimise noise transmission.

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