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Solve a system of 4 non-linear equations?

GROUPS:

I'm trying to use Wolfram|Alpha to solve a simple system of 4 non-linear equations. However, when I type in the equations it only pops out an equation for one of my unknown variables in terms of the other three. This is what I am typing into Wolfram|Alpha:

0=0.5D-2^(0.44A)+2^(0.567B), 0=0.5D+1.005C+2^(0.389A)-2^(0.643B), 0=0.5C+0.194A+0.321B, 0=0.5C-0.221A-0.283B

and I am only getting an output of

D = -2(1.005C+e^(0.269634A)-e^(-.445694B))

Please let me know if there is anyway to get solutions for all 4 variables, thanks!!

POSTED BY: Sabah Rezvani
Answer
4 months ago

I think the only solution is $a=b=c=d=0$. Here's why. You can solve the last two equations for $b$ and $c$ in terms of $a$: $c = 0.0531093 a$ and $ b= -0.687086 a$. Then the first two equations can be written as follows:

$$d=-2 \left(2^{-0.389578 a}- 2^{0.44 a}\right)$$ $$d= -2 \left(0.0533748 a-2.^{-0.441796 a}+2.^{0.389 a}\right)$$

A plot of these two curves shows the intersection is at $(0,0)$:

Intersection of two curves

So it appears that the only solution is $a=b=c=d=0$.

POSTED BY: Jim Baldwin
Answer
4 months ago

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