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7- The concentration of salt x in a home-made soap maker is given as a function of time by: dx dt = 37.5–3.5x At the initial time,t=0, the salt concentration in the tank is 50 g/L. a) Using Euler's method and a step size of h=1.5 min, what is the salt concentration after 3 minutes?

7- The concentration of salt x in a home-made soap maker is given as a function of time by: dx dt = 37.5–3.5x At the initial time,t=0, the salt concentration in the tank is 50 g/L. a) Using Euler's method and a step size of h=1.5 min, what is the salt concentration after 3 minutes?

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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7- The concentration of salt x in a home-made soap maker is given as a function of time by: dx dt = 37.5 – 3.5 At the initial time,t = 0, the salt concentration in the tank is 50 g/L. a) Using Euler's method and a step size of h=1.5 min, what is the salt concentration after 3 minutes? b) Using Runge-Kutta 4th order method and a step size of h=1.5 min, what is the salt concentration after 3? c) Solve the given ODE and find the exact solution. What is the salt concentration after 3 minutes calculated by the exact solution? d) Compare and discuss your results in parts a, b, and c.
Transcribed Image Text:7- The concentration of salt x in a home-made soap maker is given as a function of time by: dx dt = 37.5 – 3.5 At the initial time,t = 0, the salt concentration in the tank is 50 g/L. a) Using Euler's method and a step size of h=1.5 min, what is the salt concentration after 3 minutes? b) Using Runge-Kutta 4th order method and a step size of h=1.5 min, what is the salt concentration after 3? c) Solve the given ODE and find the exact solution. What is the salt concentration after 3 minutes calculated by the exact solution? d) Compare and discuss your results in parts a, b, and c.
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