Consider the initial value problem y=4xy+3;y(0)=6. Use Euler\'s method to find a
ID: 2880482 • Letter: C
Question
Consider the initial value problem y=4xy+3;y(0)=6. Use Euler's method to find approximate values for y at each of the points x = 0.1, 0.2, 0.3, and 0.4. Use a step size of h = 0.1. Fill in the values you obtain in the following table (calculate your values at each step to at least eight figures, and then record your answers rounded to four decimal places):
x = 0.1 --- y = ?, x = 0.2 --- y = ?, x = 0.3 --- y = ?, x = 0.4 --- y = ?
Now find approximate values for y at each of the points x = 0.1, 0.2, 0.3, and 0.4 with the smaller step size of h = 0.05 (again, calculate your values at each step to at least eight figures, and then record your answers rounded to four decimal places):
x = 0.1 --- y = ?, x = 0.2 --- y = ?, x = 0.3 --- y = ?, x = 0.4 --- y = ?
Stop and write down your answers in the two tables above; you will need them for the next problem.
I have the first four correct. The last four I need help with. This is the second time posting this. Please do not answer unless its correct. Thank you
Explanation / Answer
we take h=0.1
x=0,y=6
y=4xy+3;y(0)=6.
new y= old(y)+h(y')
the vaarious calculation are arranged as follows:
5.13343
Thus the required approximation value of y= 5.13343
b)
we take h=0.05
x=0,y=6
y=4xy+3;y(0)=6.
new y= old(y)+h(y')
the vaarious calculation are arranged as follows:
5.755942188
Thus the required approximation value of y= 5.755942188.
x y(old y) y' new y 0 6 -3 5.7 0.1 5.7 -2.3 5.47 0.2 5.47 -1.67 5.303 0.3 5.303 -1.103 5.1927 0.4 5.1927 -0.59275.13343