Question

Apply Euler’s method to approximate y(3) to the differential equation dy dx = x − y, y(0) = 1 using step size h=1.

Answer 1

Answer:

So y(3)=1

Step-by-step explanation:

Given that

$\dfrac{dy}{dx}=x-y$

y(0)=1,step size h=1

From Euler's method

$\dfrac{dy}{dx}=f(x,y)=x-y$

$y_{n+1}=y_n+hf(x_n,y_n),x_n=x_0+nh$  

$y_1=y_0+hf(x_0,y_0)$

$y_1=1+1f(0,1)$

f(0,1)=0-1= -1

$y_1=1-1$=0

$y_{2}=y_1+hf(x_1,y_1)$

$y_{2}=0+1f(1,0)$

f(1,0)=1

$y_{2}=1$

$y_{3}=y_2+hf(x_2,y_2)$

$y_{3}=1+1f(2,1)$

f(2,1)=1

$y_{3}=1+1$=2

$y_{4}=y_3+hf(x_3,y_3)$

$y_{4}=2+1f(3,2)$

f(3,2)= -1

$y_{4}=2-1$=1

So y(3)=1