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

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karthik suresh 2016-4-8

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评论： Walter Roberson 2016-4-9

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.

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James Tursa 2016-4-8

"... 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?

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Answer 1

Walter Roberson 2016-4-8

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

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John D'Errico 2016-4-8

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

Walter Roberson 2016-4-9

Ah, you are correct.

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Answer 2

John D'Errico 2016-4-8

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在 MATLAB Online 中打开

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