Series solutions to differential equation, Mathematics

Assignment Help:

Before we find into finding series solutions to differential equations we require determining when we can get series solutions to differential equations. Therefore, let's start with the differential equation,

 p (x) y′′ + q (x) y′ + r (x )y = 0                   (1)

Now there we really do mean nonconstant coefficients. For this point we've only dealt along with constant coefficients. Though, with series solutions we can now contain nonconstant coefficient differential equations. As well as, in order to make the problems some nicer we will be dealing only along with polynomial coefficients.

Here, we say that x=x0 is an ordinary point if given both,

q(x)/p(x)                      and                  r(x)/p(x)

Both are analytic at x=x0. It is to say that such two quantities have Taylor series around x=x0. Our aim is only dealing with coefficients which are polynomials thus this will be equivalent to saying as,

p(x0) ≠ 0

If a point is not an ordinary point so we call this a singular point.

The fundamental idea to finding a series solution to a differential equation is to suppose that we can write the solution like a power series in the form,

1856_Series Solutions to Differential Equation9.png..................(2)

And then try to find out what the an's require to be. We will only be capable to do this if the point x=x0, is an ordinary point. We will generally say as (2) is a series solution around x=x0.

Let's begin with a very fundamental example of this. Actually this will be so fundamental that we will contain constant coefficients. It will permit us to check that we find the exact solution.


Related Discussions:- Series solutions to differential equation

Basic set union operation, Q. Basic Set Union Operation? Ans. Supp...

Q. Basic Set Union Operation? Ans. Suppose instead that your school needs to know which students are taking either art or business or both. Then the students who are ta

Introduction to helping children learn mathematics, INTRODUCTION :  Do you...

INTRODUCTION :  Do you remember your school-going days, particularly your mathematics classes? What was it about those classes that made you like, or dislike, mathematics? In this

Parametric equations and polar coordinates, Parametric Equations and Polar ...

Parametric Equations and Polar Coordinates In this part we come across at parametric equations and polar coordinates. When the two subjects don't come out to have that much in

Four-step plan, Adison earned $25 mowing her neighbor''s lawn. Then she loa...

Adison earned $25 mowing her neighbor''s lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday. She now has $86. How much money did Adison have to

In sequence to remain the pole perpendicular to the ground, A cable is atta...

A cable is attached to a pole 24 ft above ground and fastened to a stake 10 ft from the base of the pole. In sequence to remain the pole perpendicular to the ground, how long is th

Determine the actual viewing area, Computer monitors are calculated by thei...

Computer monitors are calculated by their diagonals. If a monitor is advertised to be 19 in, Determine the actual viewing area, considerthe screen is square? (Round to the nearest

Fractions, A car travels 283 1/km in 4 2/3 hours .How far does it go in 1 h...

A car travels 283 1/km in 4 2/3 hours .How far does it go in 1 hour?

What is the average of his four quiz grades, Andy earned the subsequent gra...

Andy earned the subsequent grades on his four math quizzes: 97, 78, 84, and 86. What is the average of his four quiz grades? To ?nd out the average, you must add the items (97

Example of graphing equations, Example of Graphing Equations: Example...

Example of Graphing Equations: Example: By using the above figure, find out the distance traveled if the average speed is 20 mph and the time traveled is 40 minutes. T

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd