Trying to get this equation in terms of x

[chazwozzler]

Homework Statement

I need to have x on the LHS in terms of just y, h and t on the RHS:

Homework Equations

x = y + h(t² - x²)sin(x)

The Attempt at a Solution

I really don't know where to begin. I'm pretty sure there'll need to be an arcsin somewhere. Is this even possible?
Thanks in advance!

 

[fzero]

Oops, my mistake.

 

[chazwozzler]

I think maybe I was oversimplifying things - it's a backward Euler method:

y_n+1 = y_n + h(t_n+1² - y_n+1²)sin(y_n+1)

so I think I have to get that just in terms of y_n in order to get the algorithm.

 

[fzero]

If there's a general solution, it won't be in terms of elementary functions. If this is part of a grander numerical scheme, you can probably try to incorporate a numerical root-finding algorithm.

 

[chazwozzler]

I don't know how to do that at all. The equation is

y' = (t² - y²)siny,
y(0) = -1

and we're asked to use the backward Euler method to find approx. values for the IVP at t=0.1, 0.2, 0.3 and 0.4 with h=0.05.

I'm not very good at this algorithm thing..

 

[fzero]

You should look up the Newton-Raphson method for finding roots. You'll have to apply it at each step.

 

[chazwozzler]

OK cheers