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Equations cannot be solved by Wolfram Alpha

La Lu
Posted 1 month ago

Hello,

I tried this post solve cos(x)*cos(y)+2*x=0,-sin(x)*sin(y)+2*y=0 for x y in Wolfram Alpha in different variations (brackets used / not used, hand over arguments / variables or not) but all of them resulted in this:
enter image description here
Here's another run with the same functions.

What's the reason for that? How can I solve it?
POSTED BY: La Lu
9 Replies
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This is not a Matlab site, but the Matlab package Chebfun can probably solve your system.
POSTED BY: Michael Rogers

I don't know why Wolfram Alpha cannot handle this system. Mathematica finds the real solution this way:

ContourPlot[{Cos[x]*Cos[y] + 2*x == 0,
  -Sin[x]*Sin[y] + 2*y == 0},
 {x, -4, 4}, {y, -4, 4}]
Reduce[Cos[x]*Cos[y] + 2*x == 0 &&
  -Sin[x]*Sin[y] + 2*y == 0 &&
  Abs[x] < 2 && Abs[y] < 2,
 {x, y}, Reals]

There are complex solutions too:

Reduce[Cos[x]*Cos[y] + 2*x == 0 &&
  -Sin[x]*Sin[y] + 2*y == 0 &&
  Abs[x] < 2 && Abs[y] < 2,
 {x, y}]
POSTED BY: Gianluca Gorni
La Lu
La Lu
Posted 1 month ago

Do you know anybody who could me help solving this system whith Wolfram Alpha? I think the offical help is only for paying customers, right?

Could you please return me the output of mathematica since I've no access to it?
POSTED BY: La Lu

Sorry about Wolfram Alpha, I have no idea. The complex solutions near the origin are as follows:

In[3]:= NSolve[Cos[x]*Cos[y] + 2*x == 0 &&
  -Sin[x]*Sin[y] + 2*y == 0 &&
  Abs[x] < 2 && Abs[y] < 2,
 {x, y}]

Out[3]= {{x -> -0.450184, y -> 0.}, {x -> 0.914252 - 1.3176 I, 
  y -> -1.36444 + 1.3176 I}, {x -> 0.914252 + 1.3176 I, 
  y -> -1.36444 - 1.3176 I}}

The first solution is real and it looks the same as in Matlab.
POSTED BY: Gianluca Gorni
La Lu
La Lu
Posted 1 month ago

Thanks
POSTED BY: La Lu

With a free account, can you access

POSTED BY: Marvin Ray Burns A.G.S. (cum laude)

I don't know about Wolfram Alpha, but Mathematica gives nontrivial complex solutions too, provided we give bounds on the variables:

solY = Solve[Sin[y] + 2 y == 0 &&
    Abs[y] < 6][[2]]
Solve[Abs[x] < 2 &&
   -Sin[x]*Cos[x]*Cos[y] + 2*x == 0 /. solY, x]
POSTED BY: Gianluca Gorni
Bill Nelson
Bill Nelson
Posted 1 month ago 
Solve sin(y)+2*y=0 for y

yields y=0

Solve -sin(x)*cos(x)*cos(y)+2*x=0,y=0 for x

yields x=0
POSTED BY: Bill Nelson
La Lu
La Lu
Posted 1 month ago

I've got a typo in the equations in the post, but the link is correct.

Matlab returns: x: -0.45018361129487357303653869676269 y: 0

But I want to check, that I get all solutions. Matlab doesn't solve trigonometrical equations over R, e.g. sin(x) = 0 returns: x = 0. Wolfram does it work better, it returns: x = π n and n element Z

I've already plotted the equation above and realized that there's only one solution, but I want to do that precisely.
POSTED BY: La Lu
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