Use Euler's method with h = 0.1 to approximate y(1.0) and y(2.0) for the differential equation , .
A) -2.8343, -4.5215
B) -1.8345, -0.8317
C) -2.8969, -4.4726
D) -2.7343, -4.4215

Question

Use Euler's method with h = 0.1 to approximate y(1.0) and y(2.0) for the differential equation  ,  .
A) -2.8343, -4.5215 
B) -1.8345, -0.8317 
C) -2.8969, -4.4726 
D) -2.7343, -4.4215

Quizplus · Accepted Answer

Using Euler's method with h = 0.1, we have:

For y(1.0):
y(1.0) = y(0) + h * y'(0)
y'(0) = 4.0 - 2.0 * y(0)
y(0) = 0
y(1.0) = 0 + 0.1 * (4.0 - 2.0 * 0)
y(1.0) = 0.4

For y(2.0):
y(2.0) = y(1.0) + h * y'(1.0)
y'(1.0) = 4.0 - 2.0 * y(1.0)
y(1.0) = 0.4
y(2.0) = 0.4 + 0.1 * (4.0 - 2.0 * 0.4)
y(2.0) = 0.728

Therefore, the best choice is C, since it gives the closest values to the calculated approximations.

Use Euler's Method with H = 0