Solving Second Order Inhomogeneous Equations with ODEs

  • Thread starter Thread starter naxiaodong
  • Start date Start date
  • Tags Tags
    Second order
Click For Summary
The discussion focuses on solving the second-order inhomogeneous differential equation d²y/dx² + k*dy/dx = du/dx + u. Participants highlight that traditional methods may not suffice due to the presence of multiple functions. The method of Frobenius is suggested as a potential approach, transforming the problem into a series solution. Additionally, reworking the equation into a partial differential equation is proposed to gain insights into the relationship between variables. Ultimately, using Laplace transforms can help derive a transfer function, but requires knowledge of the input function u(x) and initial conditions for y.
naxiaodong
Messages
1
Reaction score
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
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.
 
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.
 
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.
 
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).
 

Similar threads

Undergrad Converting Second Order ODE to Hypergeometric Function
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Second Order ODE with Exponential Coefficients
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Solve the Partial differential equation ##U_{xy}=0##
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Nonlinear Second Order ODE: Can We Find an Analytical Solution?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How do I solve this first order second degree differential equation?
  • · Replies 7 ·
Replies
7
Views
4K
MHB Converting a Second-Order IVP into a System of Equations: Can Substitution Help?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Can you check the solution for this second order ODE?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Solve second order linear differential equation
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Second order non-homogeneous linear ordinary differential equation
  • · Replies 2 ·
Replies
2
Views
3K
High School Solve ODE with Fractional Term: Find Solutions
  • · Replies 2 ·
Replies
2
Views
2K