What ordinary differential equation? Simple answer is needed

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SUMMARY

The discussion centers on identifying the types of ordinary differential equations (ODEs) represented in two examples using the method of separation of variables. The first equation, du/dt = (d²u)/(dx²) - 5 du/dt, is a second-order linear ODE, while the second equation, du/dt = 2(d⁴u/dx⁴), is a fourth-order linear ODE. The method of separation of variables is crucial for solving these equations, allowing for the separation of variables to facilitate integration and solution finding.

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What ordinary differential equation? Simple answer is needed!

Homework Statement


instead [delta] i will use 'd'.
in these two example, what kind of ordinary dif. eq. are implied by the methodd of separation of variables.
first one is;

du/dt=(d^2u)/(dx^2) - 5 du/dt

and other one is;

du/dt=2(d^4u/dx^4)

'd' is [delta] in these examples...
Thanks for now..

Homework Equations





The Attempt at a Solution


 
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Well, what have you done? Since the problems refers to what you would get "by the methodd of separation of variables", what is the "method of separation of variables?
 

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