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## Main Question or Discussion Point

I've been working through an equation for awhile and finally reduced it to a differential equation I have to solve, but I'm not sure how to solve it, the equation is:

[tex]y'' + (At + B)y' + (Ct + D)y = 0[/tex]

Where t is a variable and A..D are constants. I attempted to solve this using taylor approximations and found the iterative relationship:

[tex]a_{n+2} = \frac{B(n+1)a_{n+1} + Ca_{n-1} + (An+D)a_n}{(n+1)(n+2)}[/tex]

But I don't know of any analytical functions that look anything like that. I could of course get a numeric approximation, but I need an actual analytic function. Does anybody have any suggestions on any methods which I should use in order to solve this function?

Thanks in advance,

~Lyuokdea

[tex]y'' + (At + B)y' + (Ct + D)y = 0[/tex]

Where t is a variable and A..D are constants. I attempted to solve this using taylor approximations and found the iterative relationship:

[tex]a_{n+2} = \frac{B(n+1)a_{n+1} + Ca_{n-1} + (An+D)a_n}{(n+1)(n+2)}[/tex]

But I don't know of any analytical functions that look anything like that. I could of course get a numeric approximation, but I need an actual analytic function. Does anybody have any suggestions on any methods which I should use in order to solve this function?

Thanks in advance,

~Lyuokdea