How can i find the dy/dx of the differantial equation

My differantial equation is 1/x*d/dx(x*dy/dx)=10.

And my code is below. I can solve x, y but i can not solve dy/dx, how to find dy/dx value of this problem. (My Code is correct)

function SteadyHeat1DNumeric
clc; clear;
x1=0.06; x2=0.08;
t=linspace(x1,x2,21);
tspan = [x1 x2];
xmesh = linspace(x1,x2);solinit = bvpinit(xmesh, @guess);sol= bvp5c( @heatcylinder1D, @bcfcn, solinit);
for t=linspace(x1,x2,11)
 fprintf('%12.5f',t,deval(sol,t,1));fprintf('\n')
end
function res = bcfcn(ya,yb)
global h k Ts q
res = [ya(1)-150
          yb(1)-60]; 
function g = guess(x)
g = [1 1000];
function dxdy = heatcylinder1D(x,y)
global g k 
dxdy = zeros(2,1);
dxdy(1) = y(2)/x;
dxdy(2) = 10;

Answer 1

[Bruno Luong]

"(My Code is correct)"

To me it's not. See below for the correction (the problem is I can't see it's change the solution after fixing the code, and I don't know why and did not investigated further for reason).

I give you here the code corrected + 2 methods to computs dy/dx

x1=0.06; x2=0.08;
xmesh = linspace(x1,x2);
solinit = bvpinit(xmesh, @guess);
sol= bvp5c( @heatcylinder1D, @bcfcn, solinit);

figure
hold on
plot(gradient(sol.y(1,:),sol.x),'ro-')
plot(deval(sol,sol.x,2)./sol.x,'b+-')
legend('dy/dx gradient','dy/dx deval')

function res = bcfcn(ya,yb)
res = [ya(1)-150
    yb(1)-60];
end

function g = guess(x)
g = [1 1000];
end

function dxdy = heatcylinder1D(x,y)
dxdy = zeros(2,1);
dxdy(1) = y(2)/x;
dxdy(2) = 10*x; % <= error is here
end

[esat gulhan]

Pretty answer, thank you

Answer 2

[KSSV]

You can use gradient function.

dy = gradient(y) ;
dx = gradient(x) ; 
dydx = dy./dx ;   % dy/dx 

[KSSV]

OP Commented:

I tried

for t=linspace(x1,x2,11)
fprintf('%12.5f',t,deval(sol,t,1));fprintf('\n')
dy = gradient(deval(sol,t,1)) 
dx = gradient(t) 
dydx = dy./dx 
end

But it does not work

[KSSV]

for t=linspace(x1,x2,11)
fprintf('%12.5f',t,deval(sol,t,1));fprintf('\n')
y = deval(sol,t,1)) ;
end
dy = gradient(y) ; 
dt = gradient(t) ; 
dydt = dy./dt ; 

[esat gulhan]

Unfortunately it does not work, it gives Nan

[KSSV]

y = deval(sol,t,1))

What is size of y?

[esat gulhan]

Oh size is 2. I think i find the solution. deval(sol,t,2),

thanks

Answer 3

[krishnil]

Compute∇·Fand∇×F. 1.

F(x,y,z)=x2i−2j+yzk.