The document describes a C program that uses Euler's method to solve a differential equation for values of x from 0 to 0.4 in increments of 0.05. The program calculates the value of y for each x value using the Euler method formula, printing the results to 5 decimal places. It is given that the initial value of y is 0 when x is 0.

1. EULER’S METHOD IN C
Date:-
Write a C program to solve the differential equation
for x=0(0.05)0.4By Euler method correct up to 5 decimal places,given that y=0 for
x=0
Program code:-
#include<stdio.h>
#include<math.h>
float f(float x,float y);
int main()
{
float x0,xn,y0,h;
x0=0;
xn=0.4;
y0=0;
h=0.05;
printf("t xtt yn n");
while(x0<xn)
{
y0=y0+h*f(x0,y0);
x0=x0+h;
printf("%12.5f t %12.5fn",x0,y0);
}
}
float f(float x,float y)
{
float z;
z=(1.+x*y)/(1.+10.*pow(y,2.));
return(z);
}

2. Output:-
x y
0.05000 0.05000
0.10000 0.09890
0.15000 0.14490
0.20000 0.18712
0.25000 0.22554
0.30000 0.26055
0.35000 0.29266
0.40000 0.32235