# free software for solving three equations of this type...

• Oct 23rd 2007, 01:28 AM
jeremie
free software for solving three equations of this type...
Hi everybody,
I join you because I need help (Tmi)
I want to solve three equations with three unknown values (x,y,,z) and the known constants are (a,b,c,d,e,f,g,h,i) but I would like to be able to change them easily without having to recalculate !!
The equations are from the type:
a=x*b + (((c+d)^2)/((c/(y/e)+d/(z/f))
g=y*c + (((b+d)^2)/((b/(x/h)+d/(z/f))
i=z*d + (((b+c)^2)/((b/(x/h)+c/(y/e))
I can of course simplify this equations by implementing all the known values but I would like to be able to vary these values! Some may have recognize these equations, they are for the thermal conductivity of composites with fibers in three orthotropic directions! I have values for several materials, some several constants and for each material, I want to find out x,y and z!
So, I would like to find a free software where I can put the full form of my equations and input the constants seperately!
Do you have any clue of where I can find such an "easy" software :)
Regards
Jeremie who is not able to create a software for this(Sadsmile)
• Oct 23rd 2007, 05:00 AM
topsquark
Quote:

Originally Posted by jeremie
Hi everybody,
I join you because I need help (Tmi)
I want to solve three equations with three unknown values (x,y,,z) and the known constants are (a,b,c,d,e,f,g,h,i) but I would like to be able to change them easily without having to recalculate !!
The equations are from the type:
a=x*b + (((c+d)^2)/((c/(y/e)+d/(z/f))
g=y*c + (((b+d)^2)/((b/(x/h)+d/(z/f))
i=z*d + (((b+c)^2)/((b/(x/h)+c/(y/e))
I can of course simplify this equations by implementing all the known values but I would like to be able to vary these values! Some may have recognize these equations, they are for the thermal conductivity of composites with fibers in three orthotropic directions! I have values for several materials, some several constants and for each material, I want to find out x,y and z!
So, I would like to find a free software where I can put the full form of my equations and input the constants seperately!
Do you have any clue of where I can find such an "easy" software :)
Regards
Jeremie who is not able to create a software for this(Sadsmile)

If you can solve for x, y, and z if given values for the constants, then you can apply the same methods with the variables in place.

A more primitive example of this is $\displaystyle ax^2 + bx + c = 0$.

If given a, b, and c, you can solve this using the completing the square method and get the answer. But if you leave them as constants and solve using the same method you get the quadratic formula, which is of much greater value.

-Dan
• Oct 23rd 2007, 05:35 AM
jeremie
I cant solve it so easily as ax2 + bx + c!
Hi Topsquark (Dan),

In fact I already knew how to solve y=ax2 + bx + c but the equations I displayed are more complicated in my sense since when you develop them even with the values for a,b,c...i, then you will obtain coeficcient like x*y, y*z and maybe even more complicated, I just gave up at this time!

That is why I really would like to use a software since my purpose is not really to learn how to solve but to solve :D

In this frame, do you or anyone else can futher guide me towards a software solution to my problem??

Jeremie
• Oct 23rd 2007, 07:41 AM
topsquark
Quote:

Originally Posted by jeremie
a=x*b + (((c+d)^2)/((c/(y/e)+d/(z/f))
g=y*c + (((b+d)^2)/((b/(x/h)+d/(z/f))
i=z*d + (((b+c)^2)/((b/(x/h)+c/(y/e))

These equations are simplified to
$\displaystyle a = bx + \frac{yz(c + d)^2}{ce + df}$

$\displaystyle g = cy + \frac{xz(b + d)^2}{bh + df}$

$\displaystyle i = dz + \frac{xy(b + c)^2}{bh + cy}$

Now, solve the first equation for x:
$\displaystyle x = \frac{a}{b} - \frac{yz(c + d)^2}{bce + bdf}$

Now sub this into your second and third equations:
$\displaystyle g = cy + \frac{\left ( \frac{a}{b} - \frac{yz(c + d)^2}{bce + bdf} \right )z(b + d)^2}{bh + df}$

$\displaystyle i = dz + \frac{\left ( \frac{a}{b} - \frac{yz(c + d)^2}{bce + bdf} \right )y(b + c)^2}{bh + cy}$

The top equation can be simplified:
$\displaystyle g = \frac{yc(b^2h + bdf)(ce + df) + z(ace + adf)(b + d)^2 - yz^2(c + d)^2(b + d)^2}{(b^2h + bdf)(ce + df)}$

Solve this for y and plug it into the last equation, and then you'll have an equation for z. Once you get this I'd recommend setting a new set of variables for convenience, then solve for z.

It's a lot of work, but quite doable.

-Dan
• Oct 26th 2007, 10:20 AM
jeremie
Dan,