Describing the form of a second-order D.E.

  • Thread starter joriarty
  • Start date
  • Tags
    Form
In summary, the conversation is about a person asking for help with a math assignment, specifically for pointers and an explanation of the theory to solve a question without giving away any answers. The second part of the conversation discusses finding a general and particular solution to an equation, with the expectation that the particular solution will involve a combination of e-2x cos(rx) and sin(rx) and decrease exponentially in magnitude as x increases.
  • #1
joriarty
62
0
Hi;
I'm having a little trouble with a maths assignment, could someone please give me a few pointers? Bear in mind this is an assignment, worth marks towards my course, so please don't give me any answers! I'm just not exactly sure how I should approach this question. A brief explanation of the theory that would help me solve it should help a lot.

Thanks! :smile:

Write up to three sentences on what the form of a particular solution of the following equation should be. Explain why any solution decreases exponentially in magnitude as x increases.

d2y/dx2 + 4(dy/dx) + 20y = 10e-2xcos(rx)
 
Physics news on Phys.org
  • #2
Welcome to PF!

Hi joriarty! Welcome to PF! :wink:

First find a "general solution", ie to the equation d2y/dx2 + 4(dy/dx) + 20y = 0

and then find a "particular solution" to the whole equation (which, I'm guessing, will be a combination of e-2x cos(rx) and sin(rx) ) :smile:
 

1. What is a second-order differential equation?

A second-order differential equation is a mathematical equation that involves a second derivative of a function. In other words, it is an equation that relates an unknown function with its first and second derivatives.

2. How do you describe the form of a second-order differential equation?

A second-order differential equation can be written in the form of y''(x) + p(x)y'(x) + q(x)y(x) = f(x), where y''(x) is the second derivative, p(x) and q(x) are functions of x, and f(x) is a function of x.

3. What are the types of solutions to a second-order differential equation?

The types of solutions to a second-order differential equation depend on the values of p(x) and q(x) in the equation. If p(x) and q(x) are constants, the solutions are called homogeneous. If p(x) and q(x) are functions of x, the solutions are called non-homogeneous.

4. How do you solve a second-order differential equation?

The method for solving a second-order differential equation depends on its type. Homogeneous equations can be solved using techniques such as substitution and separation of variables. Non-homogeneous equations require additional techniques such as variation of parameters or the method of undetermined coefficients.

5. What are the applications of second-order differential equations in science?

Second-order differential equations are used to model various physical phenomena, such as motion, heat transfer, and electrical circuits. They are also commonly used in engineering, biology, economics, and other fields to describe systems that involve time and change.

Similar threads

Cobertura (Coverage Tool): How to display the form
    • Programming and Computer Science
Replies
1
Views
827
Requesting guidance on Commutators & Intro QM
    • Introductory Physics Homework Help
Replies
1
Views
605
Do different forms of Green's functions give same result?
    • Differential Equations
Replies
1
Views
1K
Second Order Nonhomogenous Differential Equation
    • Differential Equations
Replies
2
Views
2K
MATLAB Solving Partial Differential Equation using Crank-Nicolson Method in MATLAB
    • MATLAB, Maple, Mathematica, LaTeX
Replies
14
Views
3K
BSc Physics: University Options for a second bachelor's degree
    • STEM Academic Advising
Replies
20
Views
387
Close to Sturm-Liouville form
    • Differential Equations
Replies
4
Views
2K
Second Order Linear D.E W/ Constant Coefficients and Zero RHS
    • Calculus and Beyond Homework Help
Replies
12
Views
1K
A Solving an ODE Eigenvalue Problem via the Ritz method
    • Differential Equations
Replies
1
Views
1K
Solving ODEs: y=xp+f(p): Show General Solution & Second Solution
    • Calculus and Beyond Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top