Second Order Differential Equations in MatLab

[nasko89]

Hey guys, I am new to PF. I need to be able to model a stiff differential equation in MatLab. I haven't used MatLab before so I am not really sure how to set the function and boundary conditions for the equation:

y'' + (2/x)*Y' = (.7/x^2)*( (y^(-1/2)) - (.067)((1-y)^(-1/2) )

y(0)=0
y'(1)=1
The zero boundary is undefined and there is a lot of singularities in the solution itself.

So far I have:

function dy = f(x,y)
y = [1 1];
k = .7;
lambda = .67;
xspan = [0 10];
ic = [0 1];
dy=[y(2); (-2/x) * y(2) + (k/(x)^2)*( (y(1)^(-1/2)) - lambda*((1-y(1)))^(-1/2) )];
[x,y] = ode15s(@f,xspan,ic);
plot(x,y(:,1),'-o')

And I am getting a an error in the command console:

? Input argument "x" is undefined.

Error in ==> f at 7
dy=[y(2); (-2/x) * y(2) + (k/(x)^2)*( (y(1)^(-1/2)) -
lambda*((1-y(1)))^(-1/2) )];

I do not know where to go from here.

 

[ilh]

Can someone help me out?You need to define the function for dy before calling it in ode15s. The syntax should be something like this: function dy = f(x,y) k = .7; lambda = .67; dy=[y(2); (-2/x) * y(2) + (k/(x)^2)*( (y(1)^(-1/2)) - lambda*((1-y(1)))^(-1/2) )];endxspan = [0 10];ic = [0 1];[x,y] = ode15s(@f,xspan,ic);plot(x,y(:,1),'-o')