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I’m writing a paper on the applications of linear differential equations[undergraduate level] could be in physics, chemistry, engineering, business..etc, since I am fairly new to doing research, can someone help me by giving ideas as to what applications would be good to include. thanks

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The second-order ordinary differential equation $$\ddot{x}+2\,p\,\dot{x}+\omega^2x=f(t)$$ describes damped forced vibrations of mass-spring systems, which is quite a topic in mechanics and has an application in automotive engineering, hopefully interesting for your purpose.


Another popular linear ODE, of order $1$, describes a model of population growth and is called logistic equation.

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Kepler's laws of planetary motion can be derived from Newton's law of gravitation and newtons laws of motion and solving the differential equations

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