Differential Equation with Boundary Conditions II

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SUMMARY

The discussion focuses on solving the second-order non-homogeneous ordinary differential equation (ODE) given by d²T/dx² + S²*T + B = 0, with boundary conditions dT/dx = 0 at x = 0 and T = T₂ at x = L. Participants suggest using substitution methods or finding the roots of the equation to derive solutions. The problem is identified as a review of differential equations in the context of heat transfer, emphasizing the need to first solve the complementary equation d²T/dx² + S²*T = 0 before seeking a particular solution.

PREREQUISITES
  • Understanding of second-order ordinary differential equations (ODEs)
  • Familiarity with boundary value problems in differential equations
  • Knowledge of complementary and particular solutions in ODEs
  • Basic concepts of heat transfer principles
NEXT STEPS
  • Study methods for solving second-order non-homogeneous ODEs
  • Learn about boundary value problems and their applications in heat transfer
  • Explore techniques for finding complementary and particular solutions
  • Review the implications of boundary conditions on differential equations
USEFUL FOR

Students and professionals in engineering and physics, particularly those focusing on heat transfer and differential equations, will benefit from this discussion.

ookt2c
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Homework Statement


[tex]d^2T/dx^2 + S^2*T+B=0[/tex]
Boundary Conditions:
[tex]dT/dx=0[/tex] @ x=0
T=T_2 @ x=L


Homework Equations





The Attempt at a Solution


I think you either have to make some type of substitution or find the roots and do it that way.


P.S. This is assignment is a review of diff eq for Heat Transfer
I took diff eq 2 years ago and haven't used is since until now but its quickly coming back to me. Just looking for someone to point me in the right direction. Thanks

Homework Statement

 
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this is a non-homogenous (though that has several different meanings) 2nd order ODE

so i would write it as
[tex]d^2T/dx^2 + S^2T=-B[/tex]

find the complementary solutinos by solving
[tex]d^2T/dx^2 + S^2T=0[/tex]

and then try and find a particular solution
 

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