Summarize the method of undetermined coefficients Do you thi

Summarize the method of undetermined coefficients. Do you think it would be possible to write a computer program to evaluate the undetermined coefficients so that one could simply enter into a computer a certain differential equation and the computer would print out the solution?

Solution

The method of undetermined coefficients is a technique to finding a particular solution to linear constant-coefficient differential equations and recurrence relations.If the nonhomogeneous equation f( x) in the second order general nonhomogeneous differential equation , then the method of undetermined coefficients can be used to obtain a particular solution

Progrm to evluate undetermined coefficients:

#include <stdio.h>
#include <stdlib.h>
#define MAXSIZE 10

void main()
{
int arr[MAXSIZE];
int i, num, power;
float x, Sum;

printf(\"Enter order for the polynomial \ \");
scanf(\"%d\", &num);
printf(\"Enter the value of x \ \");
scanf(\"%f\", &x);
printf(\"Enter %d coefficients \ \", num + 1);
for (i = 0; i <= num; i++)
{
scanf(\"%d\", &arr[i]);
}
Sum = arr[0];
for (i = 1; i <= num; i++)
{
Sum = Sum * x + arr[i];
}
power = num;

printf(\"Ploynomial generated: \ \");
for (i = 0; i <= num; i++)
{
if (power < 0)
{
break;
}
if (arr[i] > 0)
printf(\" + \");
else if (arr[i] < 0)
printf(\" - \");
else
printf(\" \");
printf(\"%dx^%d \", abs(arr[i]), power--);
}
printf(\"\ Total sum of polynomial afer evaluation = %6.2f \ \", Sum);
}