I have complex equation of the form x=(y/c1)+K*(y/c1)^n ??

I have complex equation of the form x=(y/c1)+K*(y/c1)^n ?? where c1, K, n are constants. The typical values are 90e9, 5e12 and 6.1245. i need to obtain y for a x and i need to obtain it for a range of values.

[James Tursa]

"... i need to obtain y for a x ..."

Do you mean you are trying to solve the equation for y when you are given a value of x? And you want to do this for a range of x values?

Answer 1

[Walter Roberson]

There is no analytic solution to that for n > 3. You will need to use numeric methods such as fzero()

[John D'Errico]

Actually, for n == 4, this would be solvable. The limit is n >= 5, or non-integer n that will be problematic.

[Walter Roberson]

Ah, you are correct.

Answer 2

[John D'Errico]

syms n y c1 K
E = x==(y/c1)+K*(y/c1)^n;
E0 = subs(E,{c1,K,n},{90e9, 5e12, 6.1245});

There will be multiple solutions. vpasolve finds them well enough, though fzero would also work.

vpasolve(E0(1))
ans =
685108721.21251019872317593852318

vpasolve(E0(2))
ans =
838327989.34904713260360139778459

vpasolve(E0(3))
ans =
- 727372205.91495288136399524186001 - 472855561.58678110600582657021201i

vpasolve(E0(4))
ans =
740586777.76325202886393577885394

...