Solving Second Order Inhomogeneous Equations with ODEs

In summary, the conversation discusses how to solve the inhomogeneous equation d2y/dx2+k*dy/dx = du/dx+u, and whether it is possible to use traditional methods or if the method of Frobenius should be used. It is also mentioned that the equation represents a dynamic system and that Laplace transforms can be used to find the transfer function from u to y. It is noted that in order to solve for y, the function u(x) and initial conditions must be known.
  • #1
naxiaodong
1
0
d2y/dx2+k*dy/dx = du/dx+u

anyone got a hint how to use ODE to sovle this inhomogenous equation?

Thanks a lot
 
Physics news on Phys.org
  • #2
You can't solve a single differential equation for two different functions any more than you can solve a single algebraic equation for two different numbers.
 
  • #3
I would say that you may be able to solve this using the method of Frobenius, which ultimately means that you break it down into a root series problem. Although, I believe the person above me was correct in saying that you cannot solve this using traditional methods since you have three different variables.
 
  • #4
hmm I wonder if its possibly to rework this into a partial differential equation for x that is a function of u and y, while not giving you a nice litle functionfor u and y it will give you a general idea of the solution.
 
  • #5
This equation seems to represent a dynamic system, where u is the input and y the output.
You can use Laplace transforms to get a transfer function from u to y.
To solve for y you must know the function u(x) and the initial conditions y(0) and y'(0).
 

FAQ: Solving Second Order Inhomogeneous Equations with ODEs

What is a second order equation?

A second order equation is a mathematical equation that contains a variable raised to the second power, such as x^2. It also commonly includes a first order term (x) and a constant term. It is also known as a quadratic equation.

What is the general form of a second order equation?

The general form of a second order equation is ax^2 + bx + c = 0, where a, b, and c are constants. This form is also known as the standard form of a quadratic equation.

How do you solve a second order equation?

To solve a second order equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. You can also factor the equation, if possible, or use other methods such as completing the square.

What are the types of solutions for a second order equation?

A second order equation can have two types of solutions: real and complex. Real solutions are values of the variable that make the equation true, while complex solutions involve the use of imaginary numbers.

What are the real-life applications of second order equations?

Second order equations have many real-life applications, such as in physics to model motion and in engineering to design structures. They are also used in economics to analyze supply and demand, and in chemistry to predict reaction rates.

Similar threads

I Converting Second Order ODE to Hypergeometric Function
Replies
7
Views
2K
I Second Order ODE with Exponential Coefficients
Replies
1
Views
2K
A Solve the Partial differential equation ##U_{xy}=0##
Replies
3
Views
3K
I Nonlinear Second Order ODE: Can We Find an Analytical Solution?
Replies
2
Views
3K
I How do I solve this first order second degree differential equation?
Replies
7
Views
3K
MHB Converting a Second-Order IVP into a System of Equations: Can Substitution Help?
Replies
1
Views
1K
I Can you check the solution for this second order ODE?
Replies
6
Views
2K
I Solve second order linear differential equation
Replies
7
Views
2K
I Second order non-homogeneous linear ordinary differential equation
Replies
2
Views
2K
B Solve ODE with Fractional Term: Find Solutions
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top