The solution of the differential equation

$$\ddot x \dot x = 1,$$

with $$x(0)=0$$ and $$\dot x(0)=0$$,

is given by

The solution of the differential equation

$$\ddot x - x = \cosh{t}$$,

with $$x(0)=0$$ and $$\dot x(0)=0$$, is given by

When comparing the $$RLC$$ circuit to the mass on a spring and to the pendulum, the resistor $$R$$ plays the role of