Differential Equations    02/20/16

 

During one’s study of calculus, one may encounter a peculiar set of derivatives known as Differential equations. Differential equations ae equations in which the derivative of the function is proportional to the function itself, examples including dydx=kyand dydx=y+x. These equations can not be solved through ordinary integration since we would be integrating in respect to a separate variable (yand dx), so one must use a method called separating and integrating, which involves moving the dxto the right side and all of the y’s to the left side (our first example would become dyy=kdx)and then integrate in respect to their variables. This is how the Exponential function comes into existence. Differential equations have an extensive range of application to other branches of science, particularly Physics, Economics, Biology, and Engineering. In fact, Differential Equations are so useful that there is an entire class at Universities dedicated to them that all Physics and Engineering majors must take!