Question

Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y' = 3y + 2xy, y(2) = 1. (Round your answer to four decimal places.) y(2.5) =

Answer 1

Answer:

1.5939 $($Correct upto four desimal places$)$

Step-by-step explanation:

To obtain the large value at $x_n=2.5$ with small step length $h=0.1$ and $x_0=2,y_0=1,x_n=2.5$ , where $x_n=x_0+nh$ we have to use c-programme.  The c-programme for Eular method is given below,

$#$includestdio.h$>$

float fun$($float$x$, float$y)$

${$

float $f;$

$f=3\times y+2\times x\timesy;$

return $f;$

$}$

main$()$

${$

float $a,b,x,y,h,t,k;$

printf$("\nEnter$ $x_0,y_0,h,xn:");$

scanf$("%f%f%f%f",&a,&b,&h,&t);$

$x=a;$

$y=b;$

printf$("\n x \t y \t");$

while$(x$

${$

$k=h\times fun(x,y);$

$y=y+k;$

$x=x+h;$

printf$("%0.3f\t%0.3f\n",x,y);$

$}$

$}$

which will give required answer $y(2.5)=$, correct upto four desimal places.