e/min.is pumped into thetalktank at a rate of 20empties, through a ho[in l/min].Consider a largetank that is initiallyfilled with10l ofquid. LiqiequidDenoteby V(t) the[in e] of liquidle onpressure, theliquid in the tank such thatvolumein thetank at timet. Due tothe bottom, atrate rwhich is proportional to the volumeofr = 5xV(t)(a)Write a differentialequation forV (t).(b) Find theeneralslution for this differential equation.(c)Find the particularsoluisfyirthegiven initialcondition.(extra)Wheredo ALLsolutions tend towhen t →o0? ExplхplaDBBB3145-BB36-B28F-CA6CA67-69B99B95FEFD20Feb/2021 5:00-6 10 PDTProvided1151 S21 AfiniTesti 26 b/2021 5.00-6.10 PDTProvided to JonathanJoadM151 S21 iniTesti 26/Feb/2021 56:10 PDTStribute/postS21 MiniTest1 Feb/2021 5:00-6:10 PDTNOT share/distribute/t/uploadistribute/post/upload M151 S21 MiTest1 26/Feb/2021 5:00-6:10 PDT Provided to Jonathan Jaimez-MeneProvided topost/upload M151 S MiniTest1 26/Feb/2021 5:00-6:10 PDTM151 S21 Mini Test26/Feb/2021 5:00-6.1021 MiniTest

Answered: Image /qna-images/answer/a670efce-68e1-4b8e-ae44-16c0c2ca6d98.jpg

e/min. hole on Consider a large filled with 10 l of liquid. tank at time tank that is initia Liquid is pumped into the tank at a rate of 20 itially [in e] of liquid proportional Denote by V(t) empties, through e/min]. [in 5xV(t) the volum pressure, the talk that r in the t. Due to a the bottom, at rate r which is to the volu me of liquid in the tank such (a) Write a differential equatic V (t). (b) Find the neral soluti ion for this differential equat (c) Find the olution satisfy n initial condition. (extra Where do ALL solutions. tend to wher hen t o0? Explai DBBB3145-BB36-B28 F-CA67-69B B95FEFD20 /2021 5:00-6.10 PDT 1 S21 AliniTesti 26 /2021 5:00-6:10 PDT Provided bute/post/ oad Provided to Jonathan ticulariniTest1 26/Feb/202 chare/distribute//upload- Mel S21 MiniTest1 Pob/2021 5:00-6:10 PDT Provided to Jonathan Jaimez-Men /post/upload M151 S21 MTest1 26/Feb/2021 5:00-6:10 PDT oload M151 SA MiniTest1 26/Feb/2021 5:00-6:10 PDT Provided to 51 S21 MiniTest \26/Feb/2021 5:00-6.1

e/min. hole on Consider a large filled with 10 l of liquid. tank at time tank that is initia Liquid is pumped into the tank at a rate of 20 itially [in e] of liquid proportional Denote by V(t) empties, through e/min]. [in 5xV(t) the volum pressure, the talk that r in the t. Due to a the bottom, at rate r which is to the volu me of liquid in the tank such (a) Write a differential equatic V (t). (b) Find the neral soluti ion for this differential equat (c) Find the olution satisfy n initial condition. (extra Where do ALL solutions. tend to wher hen t o0? Explai DBBB3145-BB36-B28 F-CA67-69B B95FEFD20 /2021 5:00-6.10 PDT 1 S21 AliniTesti 26 /2021 5:00-6:10 PDT Provided bute/post/ oad Provided to Jonathan ticulariniTest1 26/Feb/202 chare/distribute//upload- Mel S21 MiniTest1 Pob/2021 5:00-6:10 PDT Provided to Jonathan Jaimez-Men /post/upload M151 S21 MTest1 26/Feb/2021 5:00-6:10 PDT oload M151 SA MiniTest1 26/Feb/2021 5:00-6:10 PDT Provided to 51 S21 MiniTest \26/Feb/2021 5:00-6.1

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

e/min.
is pumped into the
talk
tank at a rate of 20
empties, through a ho
[in l/min].
Consider a large
tank that is ini
tially
filled with
10
l of
quid. Liqie
quid
Denote
by V(t) the
[in e] of liquid
le on
pressure, the
liquid in the tank such that
volume
in the
tank at time
t. Due to
the bottom, at
rate r
which is proportion
al to the volume
of
r = 5x
V(t)
(a)
Write a differenti
al
equation for
V (t).
(b) Find the
eneral
s
lution for this differe
ntial equation.
(c)
Find the particular
solu
isfyir
the
given initial
condition.
(extra)
Where
do ALL
solutions tend to
when t →
o0? Expl
хpla
DBBB3145-BB36-B28F-CA6
CA67-69B9
9B95FEFD20
Feb/2021 5:00-6 10 PDT
Provided
1151 S21 AfiniTesti 26 b/2021 5.00-6.10 PDT
Provided to Jonathan
Joad
M151 S21 iniTesti 26/Feb/2021 56:10 PDT
Stribute/post
S21 MiniTest1 Feb/2021 5:00-6:10 PDT
NOT share/distribute/t/upload
istribute/post/upload M151 S21 MiTest1 26/Feb/2021 5:00-6:10 PDT Provided to Jonathan Jaimez-Mene
Provided to
post/upload M151 S MiniTest1 26/Feb/2021 5:00-6:10 PDT
M151 S21 Mini Test26/Feb/2021 5:00-6.10
21 MiniTest

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