How to solve differential equation with MATLAB

Hi,

I have a problem related to solving differential equation. The equation is:

(3/2)lnX + 3886/x = 19

I can not solve this equation. I must find 'x' value..

How can I solve this with Matlab?

Thanks for your help.

[Torsten]

X and x are the same ?

Why is your problem related to solving a differential equation ? The equation you wrote is an algebraic equation.

Best wishes

Torsten.

Answer 1

[nancy]

Hi Torsten,

Actually I have understood the first equation and x is nearly 372000 derived. But it is a very high value and I can say it is not logical for my solution.

When I try an arbitrary value as nearly 375, the solution can be acceptable for me. 375 may be more logical for me.

That is to say; can there be a second answer of this equation?

Best regards,

[Torsten]

MATHEMATICA finds two solutions:

http://www.wolframalpha.com/input/?i=solve+1.5*LOG%5Bx%5D%2B3886%2Fx-19%3D0

Use MATLAB's "fzero" to get the smaller solution:

f=@(x)1.5*log(x)+3886/x-19;
x0=[300 400];
sol=fzero(f,x0)

Best wishes

Torsten.

Answer 2

[nancy]

Sorry.. You are right.. It is an algebraic equation, I wrote false..

And x and X are the same. I mean it is:

(3/2)lnX + 3886/X = 19

You can take care above equation.

Could you please help me and give me a clue to solve that?

Thanks for your help..

Answer 3

[Torsten]

Does this work ?

syms x
eqn = 1.5*log(x)+3886/x-19 == 0;
sol = solve(eqn,x);

The result should be some expression containing the Lambert-W-function.

Best wishes

Torsten.

Answer 4

[nancy]

Hi,

When I operate the above code, it gives an answer just like this:

sol =

exp(38/3)*exp(wrightOmega(pi*i + log(7772/3) - 38/3))

So, it doesn't give an exact solution..

What can I do at this step? I must find the X value as numerical.

[Torsten]

Does this work ?

syms x
eqn = 1.5*log(x)+3886/x-19 == 0;
sol = solve(eqn,x);
solnum = eval(sol);
disp(solnum)

Best wishes

Torsten.

Answer 5

[nancy]

Hi Torsten,

Actually I have understood the first equation and x is nearly 372000 derived. But it is a very high value and I can say it is not logical for my solution.

When I try an arbitrary value as nearly 375, the solution can be acceptable for me. 375 may be more logical for me.

That is to say; can there be a second answer of this equation?

Best regards,

Answer 6

[nancy]

Thank you very much for your helps.. It is ok.

Best wishes,