Chapter 7, Problem 44RE

To determine

To find the value of $y$ when $x=0.7$ . Using euler’ method.

Answer to Problem 44RE

The required solution is $F\left(0.7\right)=2.362$

Explanation of Solution

Given information: The equation is, $\frac{dy}{dx}=x-y$ and $y=2$ when $x=1$ .

Calculation: The required solution is obtained as,

  $\begin{array}{l}\frac{dy}{dx}=x-y\left(1,2\right)\\ dx=-0.1\\ x=0.7\end{array}$

x	y	dy/dx	$\delta x$	$\delta y$
1	2	-1	-0.1	0.1
0.9	2.1	-1.2	-0.1	0.12
0.8	2.22	-1.42	-0.1	0.142
0.7	2.362	-1.662	-0.1	0.1662

Hence, the required solution is $F\left(0.7\right)=2.362$