how to use solve

hi ; i need help

I have this equation with 2 parametres a and b

syms b x a

solve ((2*cos(x) - b*(sin(x) + sin(a*x))) == 0) %chooses 'x' as the unknown and returns

I use solve but it return

Warning: Cannot find explicit solution.

[VBBV]

Consider these input values for a and b, for which solve function cant handle the solution. In such cases, use vpasolve to solve equation numerically as recommended by Matlab

syms x real
a = 4; % assume some value
b = 1.5;  % assume value
sol=solve ((2*cos(x) - b*(sin(x) + sin(a*x))) == 0,[x]) % 

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

sol = 

0.31726439340850840945560345483897

sol = vpasolve((2*cos(x) - b*(sin(x) + sin(a*x))) == 0,[x])

sol = 

0.31726439340850840945560345483897

Answer 1

[VBBV]

syms b x a
sol=solve ((2*cos(x) - b*(sin(x) + sin(a*x))) == 0,[x a b]) 

sol = struct with fields:
    x: [2×1 sym]
    a: [2×1 sym]
    b: [2×1 sym]

%chooses 'x' as the unknown and returns
sol.x

ans = 

sol.a

ans = 

sol.b

ans = 

[VBBV]

You need to have 3 equations to solve for x , a and b. But you have only 1 eqn. Can you elaborate what you are trying to find ?

[alize beemiel]

i need to solve this equation with this parameter

cause this parameter change

[VBBV]

syms x real
a = 1; % assume some value
b = 1;  % assume value
sol=solve ((2*cos(x) - b*(sin(x) + sin(a*x))) == 0,[x]) % 

sol = 

The equation doesn't have explicit solution as warning suggests which means no closed form solution exists, However, if you consider real finite range of values for parameters a and b then you may possibly get a solution. So it depends on what range of values you consider for parameters in the equation

[alize beemiel]

this is what i want by using matlab

[alize beemiel]

thank you Sir ..for your help and your time

Answer 2

[Chunru]

There is no close form solution when a and b are arbitrary constant for the equation.

If you want to find the numerical solution of the equation with specified a and b, you can use vpasolve:

syms b x a
solve ((2*cos(x) - b*(sin(x) + sin(a*x))) == 0)

Warning: Unable to find explicit solution. For options, see help.

 
ans =
 
Empty sym: 0-by-1
 

a = 2; b=0.1;
vpasolve ((2*cos(x) - b*(sin(x) + sin(a*x))) == 0)  %chooses 'x' as the unknown and returns

ans = 

7.7984925986314595610243884059956

[alize beemiel]

i dont need numerical solution i need expression of x=with (a and b as parameters)

some one tell me to use inverse Lagrange theorem its look complicate for me ...there is another alternative or something with Matlab to solve my equation?

using nonlinear methods or something in Matlab

[Chunru]

MATLAB tell you that its solver could not find the explicit solution.

[alize beemiel]

thank you for all

i will try to use Newton Raphson Methode maybe its give me an approximate solution