Problem: The concentration of salt x in a home-made soap maker is given as a function of time by: dx = 37.5-3.5x dt 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 minutes c) Solve the given ODE and find the exact solution. What is the salt concentration after 3 mi calculate by the exact solution d) Compare and discuss your results in part a, b, and c
Problem: The concentration of salt x in a home-made soap maker is given as a function of time by: dx = 37.5-3.5x dt 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 minutes c) Solve the given ODE and find the exact solution. What is the salt concentration after 3 mi calculate by the exact solution d) Compare and discuss your results in part a, b, and c
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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Transcribed Image Text:Problem: The concentration of salt x in a home-made soap maker is given as a function of time by:
dx
= 37.5-3.5x
dt
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 minutes
c) Solve the given ODE and find the exact solution. What is the salt concentration after 3 mi
calculate by the exact solution
d) Compare and discuss your results in part a, b, and c
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