Consider the ODE X= 2-3x with nitial conditionX (to) = 1 and to =0. What is the value of thestafe X when t = 2 ?Estimate when the systemwill decay to a constant value using the timeconstant of the system2

Given = 2 - 3x ⇒ = 2 Integrating factor = = Solution is then…

Answered: Consider the ODE X=2-3x with nitial…

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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Q) Two tanks are connected as shown in figure below. Starting from time t=0 the pumping process shown in figure was applied. Find the amount of salt in each tank as a function of time. 6 L/min 10N/L sak T1 4 L/min T2 4 L/min 2 L/min 100 L pure H;0 100 L pure H,O
V2x 1 Let f be the function defined by f (x ) = | dt. Find an expression (2t – 5)6 - -2 for f'(x).
Find s' if s - (4x + 1)2 x2 - 2 S %3D
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
the answer for a should be cx^2+2 please give as much info as possible to the answer
complexify the ODE below in irder to find its particular solution y''-2y'-15y=e^(3t) cos(2t).
The table gives the annual US emissions, H(t), of "super greenhouse gases," in millions of metric tons of carbon-dioxide equivalent.¹ Let t be in years since 2000. ¹Includes HFCs (hydrofluorocarbons), PFCs (perfluorocarbons), SF6 (sulfur hexafluoride), and NF3 (nitrogen trifluoride). www.epa.gov/climate-indicators, accessed October 3, 2019. The units are Year 2002 2004 2006 2008 2010 2012 2014 The integral represents the H(t) 142.3 139.6 144.1 157.5 164.0 170.1 180.1 (a) What are the units and meaning of i 6₂1²³, H(t)dt? US emissions of hydrofluorocarbons during the period i to
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Consider the ODE X=2-3x with nitial condition x (to) = 1 and to -0. What is the value of the stafe X when t = 2 ? Estimate when the system will decay to a constant value usus the time constant of the system?