How to solve an equation with one unknown?

For example:

ss = (16*T*do)/pi*(do^4-di^4)

all variables are know except for (di). What is the code to solve it? Thanks in advance!

[John D'Errico]

Pencil and paper won't work? Do you really need MATLAB to do this? Have you tried the symbolic toolbox? (Which is like using a Mack truck to take a pea to Boston, but it will work.)

help syms
help solve

[Roger Stafford]

I like your reply, John. Pencil and paper is certainly the right way to do that problem.

[Ahmad Ghareeb]

This is just an example.

Answer 1

[Walter Roberson]

syms di
syms ss T do   %or assign numeric values to the variables
Pi = sym('pi');
eqn = ss == (16*T*do)/Pi*(do^4-di^4);
sol = solve(eqn, di)

The result you get back will be a vector of four elements, reflecting the four roots of the quartic. You can use double(sol) to see the decimal versions of the exact solutions.

Depending on what you are solving, you might encounter cases where you see outputs such as

 root(16*2^(1/2)*z^5 - 16*2^(1/2)*di^4*z - 17*pi, z, 1)
 root(16*2^(1/2)*z^5 - 16*2^(1/2)*di^4*z - 17*pi, z, 2)

The form root(f(z), z, N) selects from the set of values, z, such that f(z) = 0 -- that is, the roots of the equation. You will sometimes even see this for cubic equations and it is not uncommon for quartic equations; most quintics and above will generate root() forms.