Solve ODE with Fractional Term: Find Solutions

  • Context: High School 
  • Thread starter Thread starter knockout_artist
  • Start date Start date
  • Tags Tags
    Function Ode
Click For Summary
SUMMARY

The discussion focuses on solving the ordinary differential equation (ODE) represented by the equation 2d²u/dx² + (1/2)Lu = 0, where L is a function of x. The user seeks clarification on how to handle the term L in the context of ODEs, particularly in forming the characteristic equation. The derived characteristic equation is 2λ² + Lλ = 0, which is essential for finding the solutions to the original ODE. The discussion emphasizes the importance of transforming the equation to facilitate solution finding.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with characteristic equations in differential equations
  • Knowledge of fractional terms in mathematical equations
  • Basic calculus, specifically differentiation and integration
NEXT STEPS
  • Study methods for solving ordinary differential equations with variable coefficients
  • Explore the application of characteristic equations in ODEs
  • Learn about the implications of fractional terms in differential equations
  • Investigate numerical methods for approximating solutions to complex ODEs
USEFUL FOR

Mathematicians, engineering students, and researchers involved in solving differential equations, particularly those dealing with variable coefficients and fractional terms.

knockout_artist
Messages
70
Reaction score
2
Member advised to post homework-like problems in the homework sections
Hi,

This is equation I need to find solutions for
d2u/d2x + 1/2Lu = 0 where L(x)

I understand we can remove fraction from second term.
2 [d2 u/d2x ] + Lu = 0

now how do I find solution of this equation ?

How do we deal with L ? because usually we have Y'(dy/dx or in this case du/dx ) or Y (in this case u) in second term in an ode.

Thanks.
 
Physics news on Phys.org
knockout_artist said:
d2u/d2x + 1/2Lu = 0 where L(x)
something seems missing here?
 
ok we have to make characteristic equation out of it so I think

from this
2d2u/d2x + 1/2Lu = 0

following equation comes
2λ2 + Lλ = 0
 

Similar threads

Graduate Solve the Partial differential equation ##U_{xy}=0##
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad How to do Magnus expansion for time-dependent companion matrix?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Searching for radial part solution of Klein-Gordon type equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Nonlinear Second Order ODE: Can We Find an Analytical Solution?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad 2nd order ODE's, variation of parameters and the notorious constraint
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Does this ODE have any real solutions?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How to solve an ODE to find its solution
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Solving an ODE with power series
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Determining equilibrium solutions to differential equations
  • · Replies 16 ·
Replies
16
Views
4K