Question

Consider the differential equation dy/dt = -0.4(y - 1), with y(0) = 4. In all parts below, round to 4 decimal places. Part 1 Use n = 4 steps of Euler's Method with h = 0.5 to approximate y(2). y(2) ? Part 2 Use n = 8 steps of Euler's Method with h = 0.25 to approximate y(2). y(2) ? Part 3 Find y(t) using separation of variables and evaluate the exact value. y(2) =

          Consider the differential equation
dy/dt = -0.4(y - 1), with y(0) = 4.
In all parts below, round to 4 decimal places.
Part 1
Use n = 4 steps of Euler's Method with h = 0.5 to
approximate y(2).
y(2) ?
Part 2
Use n = 8 steps of Euler's Method with h = 0.25 to
approximate y(2).
y(2) ?
Part 3
Find y(t) using separation of variables and evaluate the
exact value.
y(2) =

Consider the differential equation
dy/dt = -0.4(y - 1), with y(0) = 4.
In all parts below, round to 4 decimal places.
Part 1
Use n = 4 steps of Euler's Method with h = 0.5 to
approximate y(2).
y(2) ?
Part 2
Use n = 8 steps of Euler's Method with h = 0.25 to
approximate y(2).
y(2) ?
Part 3
Find y(t) using separation of variables and evaluate the
exact value.
y(2) =

Added by Andrew K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/01/2023

Step 1

5, we can approximate y(2) as follows: t0 = 0, y0 = 4 t1 = 0 + 0.5 = 0.5, y1 = y0 + h * (-0.4y0 - 1) = 4 + 0.5 * (-0.4 * 4 - 1) = 4 + 0.5 * (-1.6 - 1) = 4 + 0.5 * (-2.6) = 4 - 1.3 = 2.7 t2 = 0.5 + 0.5 = 1, y2 = y1 + h * (-0.4y1 - 1) = 2.7 + 0.5 * (-0.4 * 2.7 - 1) Show more…

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Consider the differential equation dy/dt = -0.4(y - 1), with y(0) = 4. In all parts below, round to 4 decimal places. Part 1 Use n = 4 steps of Euler's Method with h = 0.5 to approximate y(2). y(2) ≈ Part 2 Use n = 8 steps of Euler's Method with h = 0.25 to approximate y(2). y(2) ≈ Part 3 Find y(t) using separation of variables and evaluate the exact value. y(2) =