Ordinary differential equations

Annihilator method

In mathematics, the annihilator method is a procedure used to find a particular solution to certain types of non-homogeneous ordinary differential equations (ODE's). It is similar to the method of undetermined coefficients, but instead of guessing the particular solution in the method of undetermined coefficients, the particular solution is determined systematically in this technique. The phrase undetermined coefficients can also be used to refer to the step in the annihilator method in which the coefficients are calculated. The annihilator method is used as follows. Given the ODE , find another differential operator such that . This operator is called the annihilator, hence the name of the method. Applying to both sides of the ODE gives a homogeneous ODE for which we find a solution basis as before. Then the original inhomogeneous ODE is used to construct a system of equations restricting the coefficients of the linear combination to satisfy the ODE. This method is not as general as variation of parameters in the sense that an annihilator does not always exist. (Wikipedia).

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C21 The annihilator approach

Another, perhaps better, method of solving for a higher-order, linear, nonhomogeneous differential equation with constant coefficients. In essence, some form of differentiation is performed on both sides of the equation, annihilating the right-hand side (to zero), so as to change it into

From playlist Differential Equations

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C25 Solving a DE with the annihilator approach

Solving for a differential equation by using the annihilator approach. Be warned, it is slightly different from the previous method (superposition approach), especially when it comes to how to handle the complimentary solution that appears in the general family of solutions.

From playlist Differential Equations

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C23 More about the annihilator approach

Finding the annihilator differential operator for other types of expressions.

From playlist Differential Equations

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C26 Example problem finding the form of the particular solution

More examples problems using the annihilator approach.

From playlist Differential Equations

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Annihilator Method 1: Real Linear Factors

ODEs: We use the annihilator method to solve y" - 2y' - 3y = b(x), where b(x) = (a) e^{2x}, (b) e^{3x}, and (c) e^{3x} + e^{-x}. We explain the method as an application of characteristic polynomials.

From playlist Differential Equations

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Example of Annihilator Method: y"-y = sin(2x)

ODEs: Using the annihilator method, find all solutions to the linear ODE y"-y = sin(2x).

From playlist Differential Equations

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C27 Example problem finding the form of the particular solution

More example problems using the annihilator approach.

From playlist Differential Equations

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C22 Simple examples finding the annihilator

Looking at example of calculating the annihilator differential operator for simple expressions.

From playlist Differential Equations

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How to use the Annihilator Method to Solve a Differential Equation Example with y'' + 25y = 6sin(x)

How to use the Annihilator Method to Solve a Differential Equation Example with y'' + 25y = 6sin(x) If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcer

From playlist Differential Operators and the Annihilator Method

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C24 Finding the differential annihilator

Example problem finding the annihilator differential operator.

From playlist Differential Equations

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Solve the Differential Equation y'' - 9y = 54 using the Annihilator Method

Solve the Differential Equation y'' - 9y = 54 using the Annihilator Method If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There are several way

From playlist Differential Operators and the Annihilator Method

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Second order differential equation: inhomogeneous problem

Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook Awesome method to solve inhomogeneous second order differential equation. The method is known as "The Annihilator Method" and is very powerful and can be quick!

From playlist A second course in university calculus.

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From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

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P Werner - Hybridization expansion based CTQMC

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From playlist Strongly correlated systems: From models to materials

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Nonhomogeneous 2nd-order differential equations

Download the free PDF http://tinyurl.com/EngMathYT A basic lecture showing how to solve nonhomogeneous second-order ordinary differential equations with constant coefficients. The approach illustrated uses the method of undetermined coefficients. I present several examples and show why t

From playlist A second course in university calculus.

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From playlist Lecture Series

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C30 Solving a linear DE by the annihilator approach

A two-part video of an example problem solving a DE by the method of variation of parameters, but first I show how it is done by the annihilator approach, first as a recap, but also to explain a bit more about the variation of parameters method.

From playlist Differential Equations

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Nonhomogeneous second-order differential equations

Free ebook http://tinyurl.com/EngMathYT A basic lecture showing how to solve nonhomogeneous second-order ordinary differential equations with constant coefficients. The approach illustrated uses the method of undetermined coefficients. I present several examples and show why the method w

From playlist Differential equations

Related pages

Differential operator | Method of undetermined coefficients | Natural number | Mathematics | Ordinary differential equation | Variation of parameters | Real number | Euler's formula