Symbolic element to equation for differentiation

Dear all,

I am trying to solve some differential equations in MATLAB and trying to solve them for x and z. But I just get the equations being printed rather than the output being solved.

a = 0.8

syms x z

x = @(x,z)((((1-(a^2))^0.5)*(((x)/(z))+((z)/(x)))*(a-1+((1-((z)/(x)))^2.25)))^-1);

dxz = diff(x,z);

syms x z

ABD = ((x)*(z)/2) + (((x)/4)*(((x)*(x)/(z)) + (z))) - ((1/8)*((((x)*(x)/(z))+ (z))^2)*asin((2*(x)*(z))/(((x)*(x)) + ((z)*(z)))));

pdBDx = diff(ABD,x);

pdBDz = diff(ABD,z);

DiffAABD = (1/2) + ((pdBDx*dxz)+pdBDz)*((1-(a^2))^0.5);

muABD = a*(1/((1-(a^2))^0.5)) * (1/(((x*x/z*z)+1)*z/2))* 0.5;

dybydt = DiffAABD/muABD

I would like to at the end have dybydt(1,1), but when I do it the output is

ans =

(4*z*(x^2 + 1)*((2*x)/5 - (x*(x^2/z^2 - 1))/5 + (4*(((4*x)/(5*z^2) - 4/(5*x))/(((4*x)/(5*z) + (4*z)/(5*x))^2*((1 - z/x)^(9/4) - 2/5)) + (9*(1 - z/x)^(5/4))/(4*x*((4*x)/(5*z) + (4*z)/(5*x))*((1 - z/x)^(9/4) - 2/5)^2))*((3*z)/4 + (3*x^2)/(4*z) - (((2*z)/(x^2 + z^2) - (4*x^2*z)/(x^2 + z^2)^2)*(x^2/z + z)^2)/(8*(1 - (4*x^2*z^2)/(x^2 + z^2)^2)^(1/2)) - (x*asin((2*x*z)/(x^2 + z^2))*(x^2/z + z))/(2*z)))/5 - (((2*x)/(x^2 + z^2) - (4*x*z^2)/(x^2 + z^2)^2)*(x^2/z + z)^2)/(10*(1 - (4*x^2*z^2)/(x^2 + z^2)^2)^(1/2)) + (asin((2*x*z)/(x^2 + z^2))*(x^2/z^2 - 1)*(x^2/z + z))/5 + 1/2))/3

I want them solved for x and z. I had also tried dybydt = @(x,z)DiffAABD/muABD also additing @(x,z) to all the equationsbut doesn't work. Your answers would be really helpful, thanks. :)

[Torsten]

Maybe you could describe in text form what you want to solve - from your code it's impossible to reconstruct.

[John D'Errico]

This is scary code. Difficult to understand what you want. You do things like:

syms x z
x = @(x,z)((((1-(a^2))^0.5)*(((x)/(z))+((z)/(x)))*(a-1+((1-((z)/(x)))^2.25)))^-1);

so you want to have x, as a function of x, so itself? Shiver.

Are you trying to solve a differential equation perhaps? At first, I thought that was what you wanted. As has been said, explain what you are trying to do, rather than just give code that means nothing, and have us try to guess what you really want from impossible to follow code.

[Venkatesh Pandian narayanasamy]

Dear All,

Thanks for the comments. I can breakdown the problem in the following way

1. I am trying to differentiate the equation for x for z(dx/dz), which is an implicit equation of x and y that can only be solved numerically.
2. Then I have the equation ABD( ((x)*(z)/2) + (((x)/4)*(((x)*(x)/(z)) + (z))) - ((1/8)*((((x)*(x)/(z))+ (z))^2)*asin((2*(x)*(z))/(((x)*(x)) + ((z)*(z)))))), where I am trying to get a partial derivative of it with respect to x and z as x and z are dependent and load them into DiffABD.
3. muABD is a different equation dependent on x and z and finally equate them all together to dybydt.
4. I try now to find values for dybydt at different x and z.

I could make it simpler by applying the sample algorithm to the equations below.

clear all

close all

a = 0.8

syms x z

x = @(x,z)((2*x)+z)

dxz = diff(x,z)

syms x z

ABD = @(x,z)(x) + (z)

pdBDx = diff(ABD,x)

pdBDz = diff(ABD,z)

DiffAABD = (pdBDx*dxz)+pdBDz

muABD = x + 2*z

dybydt = @(x,z)DiffAABD/muABD

dybydt(1,1) %this is what I am trying to find.

[Torsten]

The first point of the description of your task is totally weird:

I am trying to differentiate the equation for x for z(dx/dz), which is an implicit equation of x and y that can only be solved numerically.

What is the equation for x ? x = 2*x + z ?

[Venkatesh Pandian narayanasamy]

The equation for x would ideally be x = @(x,z)((((1-(a^2))^0.5)*(((x)/(z))+((z)/(x)))*(a-1+((1-((z)/(x)))^2.25)))^-1); but for simplication I tried x = @(x,z)((2*x)+z).

[Torsten]

x can not be a function of x.

[Bjorn Gustavsson]

@Venkatesh Pandian narayanasamy, maybe it will be clearer if you use mathematical notation in your problem-description. The editor has latex-like capabilities (latext-like: most/all stuff I've tried to write have worked)

[Steven Lord]

The equation for x would ideally be x ...

No, that is your implementation. Please show us the mathematical equation you're trying to solve (equations not code.) You can use the equation editor (the Sigma sign in the Insert section of the toolstrip of the comment box) to enter it, or you could attach an image of the equation if it's from a book or paper.