Solving an nonlinear equation

[pancho_hideboo]

The next step you missed: c must be zero.

In the present case,
the right hand side does not have a solution in x except the trivial solution of c=0

Very nonsense.

Do you think c=0 has any meaning ?

c=0 means that we completely ignore RHS.

Your appends simply result in raising confusion for amirhossein20.

Real number solution for x can never exist for this nonlinear equation as far as a, b, and c are all real number.

 

[albbg]

yes a,b,c are real

and x is complex in form of Q+jk , for exapmle.

sorry for the confusion. I presumed (wrongly) that x was real. If it is, instead, complex the solution can exists, but to find it in a closed form is quite difficult. The procedure is always the same: find real and imaginary parts of both lhs and rhs and equate in a system of two equations:

real(lhs)=real(rhs)
imag(lhs)=imag(rhs)

where Q and K will be the two unknowns

We know that exp(a+jb)=exp(a)*cos(b)+j*exp(a)sin(b) then:

exp(-2x)=exp(-2Q)*cos(-2K)+j*exp(-2Q)*sin(-2K)
exp(2x)=exp(2Q)*cos(2K)+j*exp(2Q)*sin(2K)

We know also that cos(z)=cos(-z) and sin(z)=-sin(-z) thus:

exp(-2x)=exp(-2Q)*cos(2K)-j*exp(-2Q)*sin(2K)
exp(2x)=exp(2Q)*cos(2K)+j*exp(2Q)*sin(2K)

but now is very difficut to proceed to obtain a closed form solution

 

[amirhossein20n]

i wanna clear some thing :

for solvig this equa, we can do numerically and analitically , ok , when you offer that transpose to the other side and plot ,so it make numeric solution such as interpolation , newton ... .
but for analitical solve , because i neeed x=x(c) function i think we need to inverse the first function i write in first post
that change c=c(x) to x=x(c) .
in other words, we dont need solve this exactly . just by inversing the first function we reach to the x=x(c) that is suficient for us .

 

[amirhossein20n]

yes of course

thanks so much

 

[pancho_hideboo]

Analytical solution, that is, closed form solution can not exist for your nonlinear equation.

Surely see https://www.edaboard.com/threads/356974/#5

 

[amirhossein20n]

can you explain what does the codes do,please ?

- - - Updated - - -

i mean inversing i need

for example this :


simply

 

[pancho_hideboo]

i mean inversing i need

Can you understand my appends ?

Analytical solution, that is, closed form solution can not exist for your nonlinear equation.

 

[amirhossein20n]

ok , you wanna say we cant write this structure for my case ??
can this function solve my equa?

 

[pancho_hideboo]

Can you understand my appends ?

Analytical solution, that is, closed form solution can not exist for your nonlinear equation.

you wanna say we cant write this structure for my case ??

I can not understand what you want to mean at all.
What do you mean by "this structure" ?
Describe correctly.

can this function solve my equa?

What do you mean by "equa" ?
Don't use unfamiliar abbreviation.

Analytical solution, that is, closed form solution can not exist for your nonlinear equation.

Can you understand a meaning of analytical solution or symbolic solution ?

However we can solve your nonlinear equation numerically while varying c value.

 

[amirhossein20n]

what's this program, you used ??

(i didnt seen mathematical program with dark black background, so far)

 

[pancho_hideboo]

what's this program, you used ??

Surely read https://www.edaboard.com/threads/356974/#10

 

[c_mitra]

Real number solution for x can never exist for this nonlinear equation as far as a, b, and c are all real number.

You appear to forget that zero is also a real number.

 

[pancho_hideboo]

You appear to forget that zero is also a real number.

No.
c=0 results in a meaningless solution.
We have to consider a!=0, b!=0 and c!=0 for solutions which have meaning.

All your and albbg's appends don't hit point at all but simply cause confusion for amirhossein20.

 

[amirhossein20n]

thanks my friends your tips was helpful