How Can I Solve This Complex Differential Equation?

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In summary, The speaker is discussing their progress in solving a special problem involving the N.-St.-equation. They have successfully solved the equation for the 2 velocity components and separated the 3rd component. They used a Bessel function to solve one term of the separation and now have a second term that looks like h[z]'' - 2 α Tan(z) h[z]' + ((λ*2α)/c2 - 1/Cos[z]^2) h[z] = 0. The speaker mentions using Maple, Mathematica, and Wolfram Alpha to solve the equation, with Mathematica now providing a solution. They will double check their equation and transformations before confirming their solution. They also mention that additional information
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w00dy85
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Hi everone, i am trying to Solve the N.-St.-equation for a special problem - i was able to solve my equation for the 2 velocity components - the 3rd velocity component i seperetated - one term of the Seperation i was able to solve with a Bessel function, the 2nd term now looks like this:

h[z]'' - 2 α Tan(z) h[z]' + ((λ*2α)/c2 - 1/Cos[z]^2) h[z] = 0

h[z] = ?
 
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  • #2
Maple solves your ODE via Legendre functoins.
 
  • #3
thank you

i tried also to solve it with mathematica or wolfram alpha - i now get an solution, what is a little bit strange, because the last few days mathematica was not able to solve my equation, probably all my transformations of the equation were useful - i hope so, but i am afraid, that i made a small mistake somewhere !

I will controll my equation and the transformation steps tomorrow, then i will know if i posted the correct form of the formula here !

But still, in case the posted formula is correct, some more Information how to solve the equation would be useful
 

FAQ: How Can I Solve This Complex Differential Equation?

What is a "real hard" differential equation?

A "real hard" differential equation is a differential equation that is particularly challenging to solve due to its complexity or the techniques required to solve it. These types of equations often involve high-order derivatives, non-linear terms, or combinations of multiple variables.

What techniques are typically used to solve real hard differential equations?

Some common techniques used to solve real hard differential equations include separation of variables, variation of parameters, Laplace transforms, and numerical methods such as Euler's method or Runge-Kutta methods. Other advanced techniques may also be used depending on the specific equation.

What are some real-world applications of real hard differential equations?

Real hard differential equations have a wide range of applications in fields such as physics, engineering, economics, and biology. They can be used to model complex systems and phenomena such as population growth, chemical reactions, heat transfer, and fluid dynamics.

How can I improve my skills in solving real hard differential equations?

Improving your skills in solving real hard differential equations requires a strong foundation in calculus, algebra, and other mathematical concepts. Practice and persistence are also key, as solving these equations often requires trial and error and multiple attempts with different techniques.

Are there any resources available for learning more about real hard differential equations?

Yes, there are many resources available for learning more about real hard differential equations. These include textbooks, online courses, video tutorials, and problem-solving guides. It can also be helpful to seek out a mentor or join a study group to get support and guidance while learning these challenging equations.

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