They have many applications in almost all areas of physics.
For example in physics-electric circuits the differential equation that governs the behaviour of a RLC circuit with a resistor of ohmic resistance R, Capacitor of capacitance C and inductor of inductance L, all in series, which is driven by a voltage source V(t) is given by ##\frac{q}{C}+R\frac{dq}{dt}+L\frac{d^2q}{dt^2}=V(t)##. q(t) is the charge of the capacitor C at time t.
Another example in physics-mechanics, the damped harmonic oscillator with mass m, spring constant k, and damping coefficient c, that is driven by an external force F(t) follows the 2nd order linear ordinary differential equation:
##m\frac{d^2x}{dt^2}+c\frac{dx}{dt}+kx=F(t)##. x(t) is the displacement of mass m at time t.
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