Solve second-order ODE with Robin boundary condition

Hello,

I would like to solve the following ODE equation with boundary conditions. A,B,C and a,b are constants.

I already wrote the odefun as below :

function dy = odefun(x,y)

dy = zeros(2,1);

dy(1) = y(2);

dy(2) = (2/(x^2))*y(1)-(2/x)*y(2);

end

Afterwards, should I use ODE45 or dvp4c or another solver ? How can I apply boundary condtion to the solver ?

At the end, I want to plot dydx in y-axis versus x in x-axis. How can I deal with this ?

I'd appreciate your help !

Answer 1

[Torsten]

syms x y(x) A B C a b
dy = diff(y,x);
eqn = diff(x^2*dy,x)-2*y == 0;
cond1 = A*dy(a)+B*y(a)/a == 0;
cond2 = A*dy(b)+B*y(b)/b == C;
conds = [cond1,cond2];
sol = dsolve(eqn,conds)

sol = 

[Qian]

It's great ! Thank you Torsten.