Solving Equation Sinus: Best Software & Arguments

[Deuskull]

Good morning everyone,

I'm working on an equation like :
a.sin(x(1+k))+b.sin(x(1-k))-c.sin(x) = 0
where x is the variable and the others one (a,b,c,k) are constant.

I tried to solve it manually but I didn't find any simple solutions.
I tried to solve it using some softwares (Mathematica and Matlab) using solve, nsolve and dsolve but without success.

What's the best software and/or the best argument (xsolve) to use ?
I want to find the analytical solution or, if it's not possible, I would like to have 10 positive numerical solutions.

Thank you.

PS : For anyone interested, this equations is a prior to use an equation of diffusion in porous material.

a = 5,95E-01
b = 5,22E-02
c = -3,53E-01
k = 0,14

 

[NemoReally]

I'm not sure that there is an analytic solution ... I suspect that it's in it's simplest form already.

I may not have understood the problem, though. It seem as though any of the mathematical applications should handle giving you values as it looks as though you have, implicitly, a straightforward function of x. For example, implementing it in Mathcad gives the following ...

 

[Bill Simpson]

In[1]:= a=5.95*10^-1;
b=5.22*10^-2;
c= -3.53*10^-1;
k=0.14;
f=a*Sin[x(1+k)]+b*Sin[x(1-k)]-c*Sin[x];
Plot[f,{x,0,25}]

Out[6]= <plot snipped>

By inspection pick starting points "near" each of the roots

In[7]:= Map[FindRoot[f==0,{x,#}]&, {0,3,6,9,12,14,17,20,22,24}]

Out[7]= {{x -> 0.}, {x -> 2.9177220113446776}, {x -> 5.822871346236126}, {x -> 8.701118634689632}, {x -> 11.534799430135319}, {x -> 14.302537173735368}, {x -> 16.98315627393366}, {x -> 19.56859265877026}, {x -> 22.08324005185527}, {x -> 24.587711402920295}}

 

[NemoReally]

Silly me ... didn't read the question properly. A Mathcad solution validating the Mathematica one:

 

[Deuskull]

Thank you for your answers.

I was too much trying to find a solution that I didn't plot the curve.
I will try to take all the roots and implement them in my next equation.

Have a good day !