Undetermined coefficients, Mathematics

Assignment Help:

In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation.

y′′ + p (t ) y′ + q (t ) y = g (t)

One of the major advantages of this method is that this reduces the problem down to an algebra problem. The algebra can find messy on occasion, but for mainly of the problems this will not be terribly difficult. The other nice thing about this method is that the complementary solution will not be explicitly needed, although as we will notice knowledge of the complementary solution will be required in some cases and so we'll generally determine that easily.

There are two drawbacks to this method. First, this will only work for a fairly small class of g(t)'s. The class of g(t)'s for that the method works, does comprise some of the more common functions, though, there are many functions out there for that undetermined coefficients simply won't work. Second, this is generally only helpful for constant coefficient differential equations.

The method is fairly simple. All that we require to do is look at g(t) and make a guess as to the form of YP(t) leaving the coefficients undetermined and thus the name of the method.  Plug the guess in the differential equation and notice if we can find out values of the coefficients. If we can find out values for the coefficients then we guessed properly, if we can't get values for the coefficients then we guessed imperfectly.

This is usually simple to notice this method in action quite than to try and describe it, therefore let's jump in some illustrations.


Related Discussions:- Undetermined coefficients

Variation of parameters, In the previous section we looked at the method of...

In the previous section we looked at the method of undetermined coefficients for getting a particular solution to p (t) y′′ + q (t) y′ + r (t) y = g (t)    .....................

Argument, what is the difference between argument and principle argument

what is the difference between argument and principle argument

Heat loss in a cylindrical pipe, which laws of physics are used to discuss ...

which laws of physics are used to discuss heat loss in a pipe

Cartesian product-categories of multiplication, Cartesian product - situat...

Cartesian product - situations in which the total number of ordered pairs (or triples, or ...) are do be found. (e.g., if Hari makes 'dosas' of 3 different sizes, with 4 different

Original price of the mittens was $10 what is the new price, A pair of mitt...

A pair of mittens has been discounted 12.5%. The original price of the mittens was $10. What is the new price? Find 12.5% of $10 and subtract it from $10. Find out 12.5% of $10

Erin is painting a bathroom what is the area to be painted, Erin is paintin...

Erin is painting a bathroom along with four walls each measuring 8 ft through 5.5 ft. Ignoring the doors or windows, what is the area to be painted? The area of the room is the

Give the example of exponents, Give the example of Exponents? When a nu...

Give the example of Exponents? When a number is multiplied several times, it is easier to write it as an exponent. For example, four multiplied to itself three times, is writte

Parent, Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbl...

Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbles as Sam?

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