From differential equations to difference equations

The most popular, widely used method in regards to solving first order linear equations is through induction. However there are similar techniques that can be employed to obtain a general solution without the use of mathematical induction. Also, general solutions can be provided by borrowing a method based on the characteristic equation for second order linear difference equations of the Euler-Cauchy type. These differential equations are an important aspect of learning as they provide a fundamental foundation of tools and intuition that lead to partial differential equations which are used to describe phenomena in natural sciences.