Differential Equation
Not what you're looking for?
Evaluate the fundamental solution of the equation u^(4) - 2u'' + u. More in general, evaluate the fundamental solution of u^(4) - (m+1)u'' + mu, where m>=0.
Please note that you are not solving the equation set equal to zero. Since you are looking for the fundamental solution you set the equation equal to the delta distribution delta_0. So you have to use the Fourier Transform in distribution sense.
Purchase this Solution
Solution Summary
This posting uses the Fourier Transform in distribution sense.
Solution Preview
To find fundamental solution we need to solve the following equation for function :
We take Fourier transform of both sides of the equation.
.
Recall the property of Fourier Transform: . Hence denoting , and using the fact that Fourier transform of delta-function is we ...
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.