i need your help...i had to solve some ode using the frobenius method but half-way through i stuck...
for the first ode
i didn't know what to do when i had to multiply the sinx and cosx with y,y',y"
ii)i had a problem because of the cosx and i couldn't equate the series...--->second ode...
My problem: find the first solution and use it to find the second solution for
x^2*y"-x*y'+(x^2+1)y=0
assuming y=summation from n=0 to infinity for An*x^n+r
substituting and solving gives me r=1 and a general equation: An=A(n-2)/((n+r)*(n+r-2)+1) for n >= 2
plugging r into my...
Somebody please help, I'm not sure I know what is going on with this.
My problem: find the first solution and use it to find the second solution for
x^2*y"-x*y'+(x^2+1)y=0
assuming y=summation from n=0 to infinity for An*x^n+r
substituting and solving gives me r=1 and a general...
does anyone know a proof for the solution to the frobenius problem for n=2? that is, that the smallest not possible number expressable as a linear combination of a and b is (a-1)(b-1)??
This is another question I have trouble proving:
Suppose the coefficients of the equation: w'' + p(z)w' + q(z)w = 0 are analytic and single-valued in a punctured neighborhood of the origin. Suppose it is known that the function w(z) = f(z) ln z is a solution, where f is analytic and...
I need to solve a linear, second order, homogeneous ODE, and I'm using the Frobenius method. This amounts to setting:
y = \sum_{n=0}^{\infty} c_n x^{n+k}
then getting y' and y'', plugging in, combining like terms, and setting the coefficient of each term to 0 to solve for the cn's. This...
Hi I'm in the process of proving a matrix norm. The Frobenius norm is defined by an nxn matrix A by ||A||_F=sum[(|aij|^2)^(1/2) i=1..n,j=1..n] I'm having trouble showing ||A+B|| <= ||A|| + ||B||
thanks for the help