Exercise $5$

The general solution to the differential equation $\frac{dy}{dx}=11x-16x^2+13cos(x)$ is

$y(x)=\frac{11}{2}{x}^2-\frac{16}{3}{x}^3+13sin(x)+C,$ 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 $0x5,$ with initial conditions $y(0)=110,180,270.$

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$)$:Plot the graphs in the same window and use different color and$/$or line$-$styles for each graph. To plot the graphs in the same window you can use the command hold on or use the plot command similarly to Exercise $4.$Add the title 'Solutions to dy$//$dx$=11$ x$-16$x$^(2)+13$ cos$($x$)\text{'}.$Add a legend with the list of C values used for each graph.$($Type help plot for a list of the different line$-$styles, and help legend for help on how to add a legend.$)$ Include both the M$-$file and the plot in your report.NOTE: the only output of the script file should be the graph of the three curves. Make sure you use enough points so that the curves are nice and smooth.