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A chemical compound decays over time when exposed tion to the power of 3/2. At the same time, the compound is produced by another process. The dif- ferential equation for its instantaneous concentration is: dn(1)-0.8n/2+10n, (1-³) where n() is the instantaneous concentration and n, 2000 is the initial concentration at 0. Solve the differential equation to find the concentration as a function of time from r-0 until - 0.5 s, using Euler's implicit method and Newton's method for solving for the roots of a nonlin- car equation. Use a step size of h 0.002 s, and plot n versus time. dt

A chemical compound decays over time when exposed tion to the power of 3/2. At the same time, the compound is produced by another process. The dif- ferential equation for its instantaneous concentration is: dn(1)-0.8n/2+10n, (1-³) where n() is the instantaneous concentration and n, 2000 is the initial concentration at 0. Solve the differential equation to find the concentration as a function of time from r-0 until - 0.5 s, using Euler's implicit method and Newton's method for solving for the roots of a nonlin- car equation. Use a step size of h 0.002 s, and plot n versus time. dt

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Example 10-2: Solving a first-order ODE using Euler's implicit method. A chemical compound decays over time when exposed to air, at a rate proportional to its concentra- tion to the power of 3/2. At the same time, the compound is produced by another process. The dif- ferential equation for its instantaneous concentration is: dn(1) --0.8m/2+10n, (1-³) dt where n(t) is the instantaneous concentration and n - 2000 is the initial concentration at 0. Solve the differential equation to find the concentration as a function of time from -0 until - 0.5 s, using Euler's implicit method and Newton's method for solving for the roots of a nonlin- car equation. Use a step size of h= 0.002 s, and plot n versus time.
Transcribed Image Text:Example 10-2: Solving a first-order ODE using Euler's implicit method. A chemical compound decays over time when exposed to air, at a rate proportional to its concentra- tion to the power of 3/2. At the same time, the compound is produced by another process. The dif- ferential equation for its instantaneous concentration is: dn(1) --0.8m/2+10n, (1-³) dt where n(t) is the instantaneous concentration and n - 2000 is the initial concentration at 0. Solve the differential equation to find the concentration as a function of time from -0 until - 0.5 s, using Euler's implicit method and Newton's method for solving for the roots of a nonlin- car equation. Use a step size of h= 0.002 s, and plot n versus time.
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