matlab - Error in Ordinary Differential Equation representation -

update trying find lyapunov exponents given in link le. trying figure out , understand taking following eqs case. these set of ordinary differential equations (these testing how work cos , sin ode)

f(1)=alpha*(y-x); f(2)=x*(r-z)-y; f(3) = 10*cos(x); 

and x=x(1); y=x(2); cos(y)=x(3);

f1 means dx/dt;f2 dy/dt , f3 in case -10sinx. however,when expressing x=x(1);y=x(2);i unsure how express cos.this trial example doing know how work equations have cos,sin etc terms function of variable.

when using ode45 solve these eqs

[t,res]=sol(3,@test_eq,@ode45,0,0.01,20,[7 2 100 ],10); 

it throws following error

??? attempted access (2); index must positive integer or logical.

error in ==> eq @ 19 x=x(1); y=x(2); cos(x)=x(3);  

1. is representation x=x(1); y=x(2); cos(y)=x(3); alright?
2. how resolve error? thank you

no representation wrong. can't possibly set values in way! start, trying assign value x(3) function.

first not sure understand difference between

x=4 

and

4=x 

which different meanings. if understand this, you'll see can't possibly assign using cos(x)=x(3).

second: function sol() calling? have defined it?

third, solve or evaluate odes should using deval or solve functions in matlab. files should give examples.