Differential Equations are one of the most useful tools developed in mathematics. You'll see them everywhere in Engineering, Physics, Biology, etc. for the modelling of phenomena.
So what are differential equations?
Well, we're used to using algebra to solve for an unknown variable. With differential equations, we use calculus to solve for an unknown function.
A differential equation is any equation that contains the derivative of an unknown function. Sometimes it is not possible to find a solution to the function due to the complexity of the equation. When a differential equation is solvable, this is usually an infinite number of solutions.
In this video, we recap some of the basic mechanics behind differential notation, where df/dx are separable. This is very useful for solving basic differential equations.
We then solve 2 of the simplest forms of differential equation:
f'(x) = 3x2 + 4x + 1
An application of finding the solution to the simplest form of differential equations - We find the solution to the displacement as a function of time of an object with constant acceleration a, initial velocity u, and initial displacement s(0) = 0.
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