Answer:
y(20)=14,322
Step-by-step explanation:
We need to solve the equation:
[tex]dy/dx=0.4xy[/tex]
with initial point
[tex]y(0) = 2[/tex]
with incerments
[tex]\Delta x=h=5[/tex]
By Euler's method, we have:
[tex]y(x+h)=y(x)+h*f'(x,y)[/tex]
We start with the initial point
[tex]y(5)=y(0)+5*f'(0,2)=2+5*(0.4*0*2)=2[/tex]
And we continue until we reach the value for y(20)
[tex]y(10)=y(5)+5*f'(5,2)=2+5*(0.4*5*2)=2+20=22\\\\\\y(15)=y(10)+5*f'(10,22)=22+5*(0.4*10*22)=22+440=462\\\\\\y(20)=y(15)+5*f'(15,462)=462+5*(0.4*15*462)=462+13,860\\\\y(20)=14,322[/tex]
