Question

Use Euler’s method to estimate the value of y(20). Use a step size of ∆x = 5. Please fill out the remainder of the chart completely. Please round everything to 4 decimal places. dy dx = 0.4xy, y(0) = 2

Answer 1

y(20)=14,322

Explanation:

We need to solve the equation:

`dy/dx=0.4xy`

with initial point

`y(0) = 2`

with incerments

`\Delta x=h=5`

By Euler's method, we have:

`y(x+h)=y(x)+h*f'(x,y)`

We start with the initial point

`y(5)=y(0)+5*f'(0,2)=2+5*(0.4*0*2)=2`

And we continue until we reach the value for y(20)

`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`