Answer to Question #248824 in Electrical Engineering for Alock kumar

Question

Write down a C program to find the solution of following ordinary differential equation using modified Euler Method and correct up to ten decimal points

dy/dx = y

Answer 1

e have 0

1 ( ) x

xy x y dx    

First approximation. Put y  1 in y  x, giving

0

2

1 1 (1 ) 1 /2 x

xy x dx x x       

Second approximation. Put y  1  x  x2/2 in y  x, giving

0

2 2 3

1 1 (1 /2) 1 /6 x

xy x x dx x x x         

Third approximation. Put y 1  x  x2  x3/6 in y  x, giving

0

3 4

2 3 2

3 1 (1 /6) 1 2 3 24

x

x

x x y x x x dx x x           

Fourth approximation. Put y  y3 in y  x, giving

3 4

2

4 0

3 4 5

2

1 1 2 3 24

1 3 12 120

x x x y x x dx

x x x x x

