Problem $1(13$ points$)$

$y$ is a function of $x.$ They have the following relationship,

$y=A{x}^2+\frac{B}{y+C}$

where $A=2,B=3,$ and $C=4.$ Generate a plot of $y$ versus $x$ for $0x1.$

Requirements:

Write a main program and a function program.

Use the Bisection method to find the value of $y$ for every value of $x.$

The Bisection Method must be written as a function program with appropriate inputs and outputs.

Main program

Define the constants.

Define a function handle for the equation that you are going to solve. The function handle has two input arguments $(x$ and $y).$

Define es corresponding to $5$ significant figures.

Define the lower and upper values as $yl=0$ and $yu=3.$

Define a vector for $x$ from $0$ to $1$ using $50$ values.

Use a 'for' loop to loop through the values of $x$ and call the function program to calculate $y$ for every value of $x.$

Generate plot of $y$ versus $x$

Function program

Use bisection method.

Here $y$ is the unknown. You should make some changes to the program in the example of the lecture.