A differential equation is one that involves a function and it's derivatives. It is often used in systems where something we are interested in is changing and the rate at which it is changing changes. To keep track of all these things which are changing we write relationships involving a function and it's derivatives.
There are two main classifications: ordinary and partial. In an ordinary differential equation we have a single independent variable. In partial differential equations there can be many independent variables.
There are general purpose solution techniques for many types of ordinary and some partial differential equations.
Real capacitors have a frequency dependent impedance characteristic. At DC they represent an infinite impedance until the voltage rises so high that the material between the "plates", the dielectric, breaks down and a spark reduces the voltage. As the frequency goes higher and higher the impedance heads for zero. When the wavelength becomes significant with respect to the dimensions of the part all sorts of unusual things happen.