Consider a tank with a solution (solute + solvent) of initial volume V0, with inflow and outflow. Keeping this solution uniformly mixed the variation of the quantity of solute in the tank, Q (t), can be obtained by resolution of the ODE below: dQ Q(t) CeVe - CsVs, Cs = dt Vo+Vet-Vst where ce is the input concentration, es is the output concentration, Ve is the input flow and V: is the outflow. Given this information, resolve the following problem. A 400-liter tank fills up with a 60kg solution of salt in water. Then water is brought into that tank at a rate of 8 L / min and the mixture, kept homogeneous by stirring, leaves the same reason. Answer: a) What is the amount of salt in the tank after 1 hour? (Find the solution solving the ODE by power series). b) Find the analytical solution for problem using MacLaurin series. * flm) (xo) (x – xo)" f(x) = D %3D n! n=0 , Xo = 0

Consider a tank with a solution (solute + solvent) of initial volume V0, with inflow and outflow. Keeping this solution uniformly mixed the variation of the quantity of solute in the tank, Q (t), can be obtained by resolution of the ODE below: dQ Q(t) CeVe - CsVs, Cs = dt Vo+Vet-Vst where ce is the input concentration, es is the output concentration, Ve is the input flow and V: is the outflow. Given this information, resolve the following problem. A 400-liter tank fills up with a 60kg solution of salt in water. Then water is brought into that tank at a rate of 8 L / min and the mixture, kept homogeneous by stirring, leaves the same reason. Answer: a) What is the amount of salt in the tank after 1 hour? (Find the solution solving the ODE by power series). b) Find the analytical solution for problem using MacLaurin series. * flm) (xo) (x – xo)" f(x) = D %3D n! n=0 , Xo = 0

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Consider a tank with a solution (solute + solvent) of initial
volume V0, with inflow and outflow. Keeping this solution
uniformly mixed the variation of the quantity of solute in
the tank, Q (t), can be obtained by resolution of the ODE
below:
dQ
Q(t)
= cęVe – C5VS , Cs =
dt
Vo+Vet-Vst
where ce is the input concentration, cs is the output
concentration, Ve is the input flow and V; is the outflow.
Given this information, resolve the following problem.
A 400-liter tank fills up with a 60kg solution of salt in water.
Then water is brought into that tank at a rate of 8 L / min
and the mixture, kept homogeneous by stirring, leaves the
same reason. Answer:
a) What is the amount of salt in the tank after 1 hour? (Find
the solution solving the ODE by power series).
b) Find the analytical solution for problem using MacLaurin
series.
f(n) (xo)
f(x) = >
n!
(x – xo)"
n=0
, X0 = 0

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