The general solution to the differential equation dy

dx $=7$x $+11$x

$2+12$ cos$($x$)$ is

y$($x$)=7$

$2$

x

$2+$

$11$

$3$

x

$3+12$ sin$($x$)+$ C with y$(0)=$ C$.$

The goal of this exercise is to write a script file to plot the solutions to the differential equation

in the interval $0<=$ x $<=9,$ with initial conditions y$(0)=590,990,1480.$

The script file should have the structure script$+$function $($similarly to the M$-$file myplot$2.$m

Example $2).$ Call the file ex$5.$m$.$ The function that defines y$($x$)$ must be included in the same file

$($note that the function defining y$($x$)$ will have two input arguments: x and C$).$

Your M$-$file should have the following structure $($fill in all the $??$ with the appropriate commands$)$:

x $=??$ ; $\%$ define the vector x in the interval $[0,9]$

y$1=$ f $(??)$ ; $\%$ compute the solution with C $=590$

y$2=$ f $(??)$ ; $\%$ compute the solution with C $=990$

y$3=$ f $(??)$ ; $\%$ compute the solution with C $=1480$

plot $(??)\%$ plot the three solutions with different line $-$ styles

title $(??)\%$ add a title

legend $(??)\%$ add a legend

function y $=$ f $($x $,$ C $)$

y $=??\%$ fill $-$in with the expression for the general solution

end