Explanation Given: y ′ = − 20 y , y ( 0 ) = 1 , y = e − 20 x h = 0.1 , 0.2 , and 0.025 Approach: Euler’s method is given by y n + 1 = y n + h f ( x n , y n ) x n + 1 = x n + h where, n = 0 , 1 , 2 , ... Calculation: f ( x , y ) = y ′ = − 20 y This implies f ( x n , y n ) = − 20 y n So, the formula for Euler’s method changes to y n + 1 = y n + h ( − 20 y n ) = ( 1 − 20 h ) y n x n + 1 = x 0 For h = 0.1 , the recursive formula is y n + 1 = y n + h ( − 20 y n ) = ( 1 − 20 × 0.1 ) y n = − y n x n + 1 = x n + 0.1 Thus, y 1 = − y 0 = − 1 x 1 = x 0 + 0.1 = 0 + 0.1 = 0.1 Therefore, y 1 = − 1 at x 1 = 0.1 y 2 = − y 1 = 1 x 2 = x 1 + 0.1 = 0.1 + 0.1 = 0.2 Therefore, y 2 = 1 at x 2 = 0.2 y 3 = − y 2 = − 1 x 3 = x 2 + 0.1 = 0.2 + 0.1 = 0.3 Therefore, y 3 = − 1 at x 3 = 0.3 ⋮ ⋮ Similarly, continue the procedure to obtain values x y 0 1 0.1 − 1 0.2 1 0.3 − 1 0.4 1 0.5 − 1 0.6 1 0.7 − 1 0.8 1 0.9 − 1 1 1 For y = e − 20 x , the actual values y ( 0 ) = 1 y ( 0

Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

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ISBN: 9780137394524

Author: R. Nagle, Edward Saff

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Differential Equations

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Chapter 3.6, Problem 17E

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The solution to y′=−20y with h=0.1,0.2,and 0.025 and compare with y=e−20x.

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Chapter 3.6, Problem 16E

Chapter 3.6, Problem 18E

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Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - A swimming pool whose volume is 10,000gal contains...Ch. 3.2 - The air in a small room 12ft by 8ft by 8ft is 3...Ch. 3.2 - Beginning at time t=0, fresh water is pumped at...Ch. 3.2 - A tank initially contains S0lb of salt dissolved...Ch. 3.2 - In 1990 the Department of Natural Resources...Ch. 3.2 - Prob. 10E

Ch. 3.2 - Prob. 11E Ch. 3.2 - For the logistic curve15, assume pa:=p(ta) and...Ch. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - 16 Show that for a differentiable function p(t),...Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - A snowball melts in such a way that the rate of...Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - During the summer the temperature inside a van...Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.4 - Prob. 1E Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 7E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 9E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - In Problem 16, let I=50 kg-m2 and the retarding...Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Rocket Flight. A model rocket having initial mass...Ch. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - An RL circuit with a 5- resistor and a 0.05-H...Ch. 3.5 - Prob. 2E Ch. 3.5 - The pathway for a binary electrical signal between...Ch. 3.5 - If the resistance in the RL circuit of Figure...Ch. 3.5 - Prob. 5E Ch. 3.5 - 6. Derive a power balance equation for the RL and...Ch. 3.5 - 7. An industrial electromagnet can be modeled as...Ch. 3.5 - 8. A 108F capacitor 10 nanofarads is charged to 50...Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - In Example 1, page 126, the improved Eulers method...Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Use the improved Eulers method subroutine with...Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Use the improved Eulers method with tolerance to...Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - The solution to the initial value problem...Ch. 3.6 - Prob. 16E Ch. 3.6 - Prob. 17E Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 20E Ch. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Determine the recursive formulas for the Taylor...Ch. 3.7 - Prob. 3E Ch. 3.7 - Prob. 4E Ch. 3.7 - Prob. 5E Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Prob. 9E Ch. 3.7 - Prob. 10E Ch. 3.7 - Prob. 11E Ch. 3.7 - Prob. 12E Ch. 3.7 - Prob. 13E Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - Prob. 16E Ch. 3.7 - The Taylor method of order 2 can be used to...Ch. 3.7 - Prob. 18E Ch. 3.7 - Prob. 19E Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E

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The solution to y ′ = − 20 y with h = 0.1 , 0.2 , and 0.025 and compare with y = e − 20 x .

Solution Summary: The author explains how Euler's method is given by yprime=-20y and compares it with y=e-20x. The choice of step size does matter since it

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To find:

The solution to y′=−20y with h=0.1,0.2,and 0.025 and compare with y=e−20x.

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Chapter 3 Solutions

The solution to y ′ = − 20 y with h = 0.1 , 0.2 , and 0.025 and compare with y = e − 20 x .

Solution Summary: The author explains how Euler's method is given by yprime=-20y and compares it with y=e-20x. The choice of step size does matter since it

Concept explainers

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To find: The solution to y′=−20y with h=0.1,0.2,and 0.025 and compare with y=e−20x.

Want to see the full answer?

Chapter 3 Solutions

To find:

The solution to y′=−20y with h=0.1,0.2,and 0.025 and compare with y=e−20x.