Integrating a 2nd order ODE

I am given an equation,

d^2y/dx^2 + q(x) = 0

x ranges from 0 to 1 and y(0) = 1 and y(L) = 1.5

where L = 1

and q(x) = 2*cos((pi*x)/L)

here is what I have

function dydx = yfunc (x,y)

x = linspace(0,1,30);
L = 1;

for i = 1:length(x)

    qx(i)= 2*cos((pi*x(i))/L);

end

dydx= -qx;

end


%main script

[x,y] = ode45(@yfunc,x,[1 1.5]);

I am running into an error stating Dimensions of arrays being concatenated are not consistent. Could you please help me?

Answer 1

[Star Strider]

This is a boundary value problem. Use bvp4c to solve it.

syms y(x) x L Y 
q(x) = 2*cos(pi*x/L);
Dy = diff(y);
D2y = diff(Dy);
ODE = D2y + q

ODE(x) = 

[VF,Subs] = odeToVectorField(ODE)

VF = 

Subs = 

bvpfcn = matlabFunction(VF, 'Vars',{x,Y,L})

bvpfcn = function_handle with value:
    @(x,Y,L)[Y(2);cos((x.*pi)./L).*-2.0]

I solved it completely, however I do not want to deprive you of the same feeling of accomplishment, so I leave the rest to you. It is a straightforward solution. Follow the examples in the documentation I linked to.

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