Solving 4th order ODE numerically with Matlab - matlab

I have been trying to solve this equation analytical, where C and L is constants:
There is no problem with the general solution, but with the conditions, the expression is close to unsolveable.
Now I'm trying to solve the problem with Matlab, where I believe i shall use the ode45 solver. I just don't know what to do with the integral and omega which is the value I'm trying to find.
I know that i haven't given any code snippet, but I just can't figure out how to solve this problem in Matlab.
I hope someone can help me, thanks.

Related

How to solve overdetermined system of equations in Matlab?

my problem is the following.
Using linsolve function I am solving an overdetermined matrix 200x50 with very similar elements. Because of this, the solution that I get is not correct. Maybe some of you would have any suggestions how to solve such a system?
Best wishes,
Valerie
It's very likely that your system does not have a solution.
Rather than attempting to solve the system A*x=b, the next best thing you can do is to solve a similar problem:
min norm(A*x-b)
When the norm used is the Euclidean norm, the solution to the minimization problem is called a "Least-Squares solution"
The MATLAB syntax is:
x = A\b

Matlab; Partial Differential Equation; ODE

I am currently trying to solve a Matlab problem. For the first part, I need to hand solve Partial Differential Equation with initial and boundary condition. However, I am lost because I don't know how to continue solving the problem after I find the equation for finding T. There is an ODE inside the boundary condition, and with that ODE, there are another initial condition. How can I link everything together? I have also attached with my work as well. Please give me some idea, thank you.enter image description hereenter image description here

How to solve a matrix optimization using MATLAB cvx

I have an optimization problem shown in uploaded figure file.
Determining the optimal matrix X maximizing given objective function is the problem.
However, since the function inside the log-function is non-concave, MATLAB CVX doesn't work.
How can I solve the problem? How should I transform the form?
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How can I implicitly solve a single equation in Matlab?

The following equation is to be solved for M by MATLAB:
(Atemp/At)^2=1/M^2*((2/(gamma+1))*(1+(gamma-1)*M^2/2))^((gamma+1)/(gamma-1))
It is not possible to solve this equation symbolically. In Maple it is easily possible to solve such an equation implicitly; now, is there also a pre-made function in Matlab that does this for me? I could program one myself, but as my skills are limited, its performance would not fit my needs.
I would try using fzero, or if that encounters problems because of complex values/infinities, fminbnd.

How can I numerically solve equations containing Bessel functions in MATLAB?

I have confronted an equation containing Bessel functions of the first type on one side and modified Bessel functions of the second type on the other. I want to know its exact solutions (values of u). The equation is as follows:
u*besselj(s-1,u)/besselj(s,u)=-w*besselK(s-1,w)/besselk(s,w)
where s is an arbitrary integer number, for example 2.
w can be written as a function of u:
w=sqrt(1-u^2);
and so this equation has only one variable: u
I'm new to MATLAB. I have no idea about how I should approach this. Could anyone please help me?
A quick thing to try may be the FZERO function, a generic nonlinear zero finder. To learn how to use it, you can implement the examples given in the documentation. Then, rewrite your function so it can be input to fzero and see what you get..
(Note: I haven't tried this, but I just noticed there were no replies yet so maybe it's better than nothing.)