Check$-$function for testing the linearity of ODEs

Step $7$ Write a $m-$file function name $y=$ CheckLinearity $($odes$,$ var$)$ that check the linearity of a given symbolic ODEs, where

odes is the given symbolic expression.

var is the symbolic expression for the function of the given odes

$y$ is boolean: true if ode is linear.

For example,

$.$

syms $x$

D $2x=$Diff$(x,1)$;

CheckLinearity $($D$2x+x,$xStep $8$ Use the technique that you learned in the class: substitute all the x and its derivatives with a dummy variable s $($use the matlab build$-$in function subs$).$ As a result, you obtain an expression like f$($s$).$

Step $9$ Check if the final expression $f(s)$ is linear respect to $s.$ This can be done by taking the first derivative of the expression with respect to $s$ and check if the resultant has any $s.$

Hint: you should use the matlab built$-$in function has for the last step.

Step $10$ Write a test script, name it testCheckLinearity, m that check the output of the function as the above test script.