A real shiny challenge has appeared for you!\ For this problem, we can use the program we developed in class to help us, In the FILES folder, you should be able to find the file euler.html, download it onto your computer.\ We set it up so that it displays the region

[-10,10]\\\\times [-10,10]

.\ Open the file up in a browser, and separately use a plain text editor to open it up to see its content. Try to understand parts of the code, such as where is

f

defined, what function is called (at the end) to plot an approximate curve, how to adjust step sizes, and how many calculations it does, etc.\ (If you like, you can write your own version, or use Excel, Numbers, GoogleSheets, etc)\ Now, for each of the following, start with the initial point

(x_(0),y_(0))=(-10,0)

. Determine which of the following differential equation will have a value

y(10)

, if starting from

y(-10)=0

.\ (a)

y^(')=(sin(x+y)+2)/(e^(x)+1)

\ (b)

y^(')=cos(y)-sin(x)-arctan(x)

\ (c)

y^(')=cos(y)-sin(x)+arctan(x)

\ (d)

y^(')=cos(y)+sin(x)+arctan(y)

\ (e)

y^(')=cos(y)+sin(x)+arctan(x)

\ (f)

y^(')=|sin(y)-0.2x|

\ (g)

y^(')=|0.2**e^(sin(x+y))|

\ (h)

y^(')=cos(y)**sin(x)

\ (i)

y^(')=cos(y)+sin(x)

\ (j)

y^(')=cos(y)+sin(x)+0.9

\ (k)

y^(')=cos(sin(x+y))

\ (I)

y^(')=sin(sin(x-y))

\ The ones that will give

y(10)

are\ (Enter all the ones that work in English alphabetical order so if you found a, b, and c, then enter abc.)\ (Note. Angles should all be in radians...)\ Note, you may need to adjust step size, number of iterations, etc. Or you can write one your own! If you do use the code, you may need to look up how to call mathematical functions in javascript.\ Hopefully you enjoy some of these cool pictures!

We set it up so that it displays the region [10,10][10,10]. Open the file up in a browser, and separately use a plain text editor to open it up to see its content. Try to understand parts of the code, such as where is f defined, what function is called (at the end) to plot an approximate curve, how to adjust step sizes, and how many calculations it does, etc. (If you like, you can write your own version, or use Excel, Numbers, GoogleSheets, etc) Now, for each of the following, start with the initial point (x0,y0)=(10,0). Determine which of the following differential equation will have a value y(10)