Consider the system of linear differential equations:
X' = AX where X is a column vector (of functions) and A is coefficient matrix. We could just as well consider a first order specific case: y'(x) = C(x)y
We know that the soltuion will be a subset of the vector space of continuous...
So how do I show that when we have a linear second-order differential equation expressed in self adjoint form that the Wronskian W(y1,y2)= C/p(x)
W=y1y2'-y1'y2, and C is a constant, and p is the coefficient where Ly=d^2/dx^2(pu) - d/dx(p1u) +p2u ?
I know Ly1=0 and Ly2= 0 if that helps at all.
I'm dealing with systems of 3 differential equations that are all coupled to each other. Fortunately, all the ODEs are first order.
Can somebody give me a primer of how to use matrices to solve these problems?
here's an example:
Say we have a system of 3 ODEs all coupled to each other...
I was wondering how coupled ODEs could be solved with Matlab.. I'm having trouble passing the coupling solution vectors between solvers since the length of the vectors isn't constant during the iteration e.g.
sol1 = bvpinit(linspace(0.,h,200),[0.1 0]);
sol2 =...
Hello and thanks in advance for anyone who can help at all. I have two problems that have stumped me.. I'm in an advanced ODE class. Here they are:
1) Consider the first order ODE f_a(x) where a is a parameter; let f_a(x0) = 0
for some solution x0 and also let f'_a(x0) != 0. Prove that...