I need help creating a C code that meets the following criteria: Develop a C-cod

Question

I need help creating a C code that meets the following criteria:

Develop a C-code to meet the requirements below:

1) Find the solution of the differential equation below by using Euler’s method. The range of x is 2 to 3.

??y/??x=??2?3?? with y=3 at x=2

2) Find the appropriate step size for this specific problem.

3) Print all the y values within the range of x=2 to x=3.

4) Solve the differential equation analytically and compare with the Euler’s method

5) Obtain a linear regression y=ax+b and show the r2 value

Your C-code must contain the following features: (1) use of arrays, (2) use of pointers, (3) use of structure, (4) use of union, (5) use of functions and function calls, (6) formatted output on screen and (7) saving of the same output on a file.

So far I have been able to create and solve the Euler's method portion of this code, but am stuck on how to continue from here. Part 4, stating how to solve the differential equation using an analytical method, and how to compare the two results using linear regression I am unsure of how to do, given that this all needs to be in one code... Any help is greatly appreciated!

Explanation / Answer

PROGRAM:

#include<stdio.h>

#include<conio.h>

#include <math.h>

double sum(double [], double [], int n);

double r(double [], double [], int , double , double );

float func(float ,float );

float euler(float ,float ,float ,int );

int main(){

double x[]={2,3};

    double y[]={3};

    double one[]={1,1};

    float xn,yo,e;

    int n=2;

    double x0=2;

    double sumx, sumy,sumxx,sumxy;

    double a,b;

    sumx=sum(x,one,n);

    sumy=sum(y,one,n);

    sumxx=sum(x,x,n);

    sumxy=sum(x,y,n);

    a=(n*sumxy-sumx*sumy)/(n*sumxx-sumx*sumx);

    b=(sumy*sumxx-sumx*sumxy)/(n*sumxx-sumx*sumx);

    printf(" By linear regression, the function is: y=%fx+%f ",a,b);

    printf(" When x= %f, y= %f ",x0,a*x0+b);

    printf(" r = %f ",r(x,y,n,a,b));

    return 0;

}

double sum(double x[],double y[], int n){

    double s=0.0;int i=0;

    for (i=0;i<n;i++)

        s=s+x[i]*y[i];

    return s;

}

double r(double x[],double y[], int n, double a, double b){

    double s0=0,s=0,ybar=0,total=0;

    int i=0;

    for (i=0;i<n;i++){

        total+=y[i];

    }

    ybar=total/n;

    for (i=0;i<n;i++){

        s0+=pow((y[i]-ybar),2);

        s+=pow((y[i]-b-a*x[i]),2);

    }

    return pow((s0-s)/s0,0.5);

    }

   printf(" inputn: ");

    scanf("%d",&n);

    printf("input x0:");           

    scanf("%f",&x0);

    printf("input xn:");

    scanf("%f",&xn);

    printf("input y0: ");

    scanf("%f",&y0);

    e=euler(x0,xn,y0,n);

}

}

float func(float x,float y){

    return ((x*x)-(3*x));

}

float euler(float x0,float xn,float y0,int n){

    float x,y,h;

    int i;

    x=x0;

    y=y0;

    h=(xn-x0)/n;

    printf("y(%f)=%6.4f ",x0,y0);

    for(i=1;i<=n;i++) {y=y+h*func(x,y);

        x=x0+i*h;

        printf("y(%f)=%6.4f ",x,y);

    }

    return y;

}

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