From the course: Complete Guide to Differential Equations Foundations for Data Science
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Euler equations
From the course: Complete Guide to Differential Equations Foundations for Data Science
Euler equations
- [Instructor] Now that you know what singular points are, let's start taking a look at solving equations involving them. First, you will take a look at a particular type of equation, Euler equations. Let's learn what these equations are. Euler equations are a type of linear differential equation with variable coefficients. They take the general form of x to the n multiplied by y of n, where the of parentheses of n denotes the derivative number. Then that's plus a of n minus one multiplied by x to the n minus one multiplied by y to the n minus one plus all the way to plus a1 multiplied by x multiplied by y prime plus a of zero multiplied by y equal to zero. It is common to find a second-order Euler equation in the following form, where you have x squared multiplied by y double prime plus a multiplied by x multiplied by y prime plus b multiplied by y equal to zero. When it comes to solving Euler equations, it is common to use their own version of a characteristic equation. So in this…
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