## How do you find the Indicial equation?

a(2r(r-1) + r) = 0 => r(2r-1) = 0, an equation which is called the indicial equation. The roots of this equation, r1 = 1/2 and r2 = 0, are called the exponents of the equation. You use each of these to write the recurrence relations in terms of n only.

## How do you use the Frobenius method?

The method is called the Frobenius method, named after the mathematician Ferdinand Georg Frobenius. x2y + P xy + Qy = 0, (5) has a singular point at x = 0, and we know that a solution for x > 0 is given by y(x) = xr = er log x, (6) where r is a root of the characteristic (or auxiliary) equation r2 + (P − 1)r + Q = 0.

## What is singular equation?

From Wikipedia, the free encyclopedia. A singular solution ys(x) of an ordinary differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution at some point on the solution.

## What is Bessel differential equation?

The Bessel differential equation is the linear second-order ordinary differential equation given by. (1) Equivalently, dividing through by , (2) The solutions to this equation define the Bessel functions and .

## What is a singular point in differential equations?

Consider a second-order ordinary differential equation. If and remain finite at , then is called an ordinary point. If either or diverges as , then is called a singular point. If either or diverges as but and remain finite as , then. is called a regular singular point (or nonessential singularity).

## What is Legendre differential equation?

Since the Legendre differential equation is a second-order ordinary differential equation, it has two linearly independent solutions. A solution which is regular at finite points is called a Legendre function of the first kind, while a solution which is singular at is called a Legendre function of the second kind.

## Why is Frobenius method used?

The Frobenius method enables one to create a power series solution to such a differential equation, provided that p(z) and q(z) are themselves analytic at 0 or, being analytic elsewhere, both their limits at 0 exist (and are finite).

## How do you find singular points?

Singular points occur when a coefficient in a particular differential equation becomes unbounded. the singular points occur where Q(x)/P(x) and/or R(x)/P(x) become unbounded.

## What is clairaut’s equation of differential equation?

Clairaut’s equation, in mathematics, a differential equation of the form y = x (dy/dx) + f(dy/dx) where f(dy/dx) is a function of dy/dx only. The equation is named for the 18th-century French mathematician and physicist Alexis-Claude Clairaut, who devised it.

## What is singular matrix?

A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0.

## What is a singular point in calculus?

A singular point of an algebraic curve is a point where the curve has “nasty” behavior such as a cusp or a point of self-intersection (when the underlying field is taken as the reals). More formally, a point on a curve is singular if the and partial derivatives of are both zero at the point . (

## What does Bessel mean?

transcendental functions expressible

You might be interested:  Pre calculus equation

## What is K in the heat equation?

It is widely used for simple engineering problems assuming there is equilibrium of the temperature fields and heat transport, with time. where u is the temperature, k is the thermal conductivity and q the heat-flux density of the source.

### Releated

#### Equation of vertical line

How do you write an equation for a vertical and horizontal line? Horizontal lines go left and right and are in the form of y = b where b represents the y intercept. Vertical lines go up and down and are in the form of x = a where a represents the shared x coordinate […]

#### Bernoulli’s equation example

What does Bernoulli’s equation State? Bernoulli’s principle states the following, Bernoulli’s principle: Within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed. Why is Bernoulli’s equation used? The Bernoulli equation is an important expression relating pressure, height and velocity of a fluid at one […]