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# Use the Laplace transform to solve the following initial value problem_y" + 4y = f (t) , y (0) = 2,y' (0) =3wheret < 2 f (t) = {2 t2 2 Procede using th...

## Question

###### Use the Laplace transform to solve the following initial value problem_y" + 4y = f (t) , y (0) = 2,y' (0) =3wheret < 2 f (t) = {2 t2 2 Procede using the following steps_ Find the Laplace transform of f (t). If Y is the Laplace transform of y; find the Laplace transform of the left side of the differential equation. Solve for Y as a function of $. Find the inverse transform of Y to solve the differential equation Write your final answer as piecewised defined function: Use the Laplace transform to solve the following initial value problem_ y" + 4y = f (t) , y (0) = 2,y' (0) =3 where t < 2 f (t) = {2 t2 2 Procede using the following steps_ Find the Laplace transform of f (t). If Y is the Laplace transform of y; find the Laplace transform of the left side of the differential equation. Solve for Y as a function of$. Find the inverse transform of Y to solve the differential equation Write your final answer as piecewised defined function:  #### Similar Solved Questions

##### Assumne that f: R + R is hounded continuous function. IF u â‚¬ C(0,1],R); deline L(u) : [0,1] + Rto be the functionL(u)(t) =1+t+,f(u(s)) dsShow that L is function from C([0.1].R) to C([0,1],2). Assume thatIf (u) - f(e)l < Qu -v for all u " â‚¬R In 2 Kum number â‚¬ < 1. Show that the equation Lu has unique solution in C([0, 1].R).
Assumne that f: R + R is hounded continuous function. IF u â‚¬ C(0,1],R); deline L(u) : [0,1] + Rto be the function L(u)(t) = 1+t+,f(u(s)) ds Show that L is function from C([0.1].R) to C([0,1],2). Assume that If (u) - f(e)l < Qu -v for all u " â‚¬R In 2 Kum number â‚¬ < 1. Sho...
##### Lety4 +22y5 _ e2x dy Use implicit differentiation to find a formula for dx
Let y4 +22y5 _ e2x dy Use implicit differentiation to find a formula for dx...
##### IentPRINTER VERSIORBACKNEXTIChapter 23 Problem 004In the figure butterfly net uniform electric field magnitude â‚¬ = 5.4 mN/C The rlm; circle of radius 7.4 cm; aligned perpendicular t0 the field The net contains no net charge_ Find the magnitude of the electric flux through the nettingNumberUnitsthe tolerance +/-29/0
ient PRINTER VERSIOR BACK NEXTI Chapter 23 Problem 004 In the figure butterfly net uniform electric field magnitude â‚¬ = 5.4 mN/C The rlm; circle of radius 7.4 cm; aligned perpendicular t0 the field The net contains no net charge_ Find the magnitude of the electric flux through the netting Numb...
##### Let R? have the inner product (u,v} 2u1Vi 2u2Vz, and let x = (2,3) and ly=(,-1) Find Ilxll; Ilyll; and | (x,y) Describe all vectors (2,,2, that are orthogonal to y Find Ilxll; Ilyl; and | (xy) Ixll (Simplify your answer Type a exact answer using radicals as needed )
Let R? have the inner product (u,v} 2u1Vi 2u2Vz, and let x = (2,3) and ly=(,-1) Find Ilxll; Ilyll; and | (x,y) Describe all vectors (2,,2, that are orthogonal to y Find Ilxll; Ilyl; and | (xy) Ixll (Simplify your answer Type a exact answer using radicals as needed )...
##### For the cunve r(t)5cos ti 5anj [2k [u 2w], find its leugth over (he giveniuterwl:The position vcetor r(t) (8t , 15 cos [5sint} describez the mxtth of A objeet hing Sce then the velocity v(t) ~pd S(ue
For the cunve r(t) 5cos ti 5anj [2k [u 2w], find its leugth over (he given iuterwl: The position vcetor r(t) (8t , 15 cos [5sint} describez the mxtth of A objeet hing Sce then the velocity v(t) ~pd S(ue...
##### QUESTION 7Use tables of critical points of the t-distributions to answer the following (give answers correct to 3 decimal places). Tobserves a t-distribution with 16 degress of freedom Find the following P(T 1.337)QUESTION 8The random variable Y1, Y2, Y53 are independent and identically distributed, with mean 0.86 and varance 0.38 What is the approximate distribution of: Y=(1/53)(Y1 Y53) N(0.86, 0.0072) N(0.86,0.38) N(0.86, 0.0847)N(0.86,0.72)
QUESTION 7 Use tables of critical points of the t-distributions to answer the following (give answers correct to 3 decimal places). Tobserves a t-distribution with 16 degress of freedom Find the following P(T 1.337) QUESTION 8 The random variable Y1, Y2, Y53 are independent and identically distribut...
##### EmeEletomcnamvctiToa Tnerier thc advortiscd movie UNNc only Jnithatttcu have through scvcral pravicw? and preprevily ad: belore thc movic Mant comou ^ that the tâ‚¬ devotcd Breviews t03 Ionq- Frellm nory sam8 0 conducted by The Wall Strrct Jourl showcd that thc standard detletion thnc emaunt ot time Cevcled prttlN5 was [htee mnutes; Ucc that Planning value for the sta ndard dovlatilon Answering (ollowing Que soonsWe Went estimate Ehc populaton mcan t Mc Deeumc 5540 conlolnceDoevictgmovlc thcate
eme EletomcnamvctiToa Tnerier thc advortiscd movie UNNc only Jnithatttcu have through scvcral pravicw? and preprevily ad: belore thc movic Mant comou ^ that the tâ‚¬ devotcd Breviews t03 Ionq- Frellm nory sam8 0 conducted by The Wall Strrct Jourl showcd that thc standard detletion thnc emaunt ot...
##### The table below shows the scores of 20 students ScoreFrequency the mean of the score is 3.5, find(a) the values of xand y (b) the mode and the median (c) the standard deviation:
The table below shows the scores of 20 students Score Frequency the mean of the score is 3.5, find (a) the values of xand y (b) the mode and the median (c) the standard deviation:...
##### One milligram of a compound of molecular weight 160 is dissolved in $10 mathrm{~mL}$ of ethanol, and the solution is poured into a $1-mathrm{cm}$ UV cell. The UV spectrum is taken, and there is an absorption at $lambda_{max }=247 mathrm{~nm}$. The maximum absorbance at $247 mathrm{~nm}$ is $0.50 .$ Calculate the value of $varepsilon$ for this absorption.
One milligram of a compound of molecular weight 160 is dissolved in $10 mathrm{~mL}$ of ethanol, and the solution is poured into a $1-mathrm{cm}$ UV cell. The UV spectrum is taken, and there is an absorption at $lambda_{max }=247 mathrm{~nm}$. The maximum absorbance at $247 mathrm{~nm}$ is $0.50 .$ ...
##### Find the position function s(t) giveu the velocity function and an initial value: "() = 40 + cost, s(0) = 3s(t) =
Find the position function s(t) giveu the velocity function and an initial value: "() = 40 + cost, s(0) = 3 s(t) =...
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Telae Lend @ 0Ju. 5 Hernntnecha Etttton Jealnleue4urastm cortyonn] HAyFudncol Rentchon Mnmcratintt olttnmall Unidahuwa â‚¬ Iho Belceshn dcmtoils lutotnUu6 D saler 0rht Bdnou Atnieanmenoke...
##### (a) Referring to Fig. $12(\mathrm{a}),$ calculate the altitude of the Sun along the meridian on the first day of summer for an observer at a latitude of $42^{\circ}$ north. FIGURE $12 \quad$ (a) The diurnal path of the Sun across the celestial sphere for an observer at latitude $L$ when the Sun is located at the vernal equinox (March), the summer solstice (June), the autumnal equinox (September), and the winter solstice (December). NCP and SCP designate the north and south celestial poles, resp
(a) Referring to Fig. $12(\mathrm{a}),$ calculate the altitude of the Sun along the meridian on the first day of summer for an observer at a latitude of $42^{\circ}$ north. FIGURE $12 \quad$ (a) The diurnal path of the Sun across the celestial sphere for an observer at latitude $L$ when the Sun is ...
##### Raindrops fall vertically at $4.5 \mathrm{m} / \mathrm{s}$ relative to the earth. What does an observer in a car moving at $22.0 \mathrm{m} / \mathrm{s}$ in a straight line measure as the velocity of the raindrops?
Raindrops fall vertically at $4.5 \mathrm{m} / \mathrm{s}$ relative to the earth. What does an observer in a car moving at $22.0 \mathrm{m} / \mathrm{s}$ in a straight line measure as the velocity of the raindrops?...
##### External toolAvailable after Sep at 11.59pm20 0f 21Roviow | Constants | Penodic Table abuntanco Uragnesium on Iha newidnel colaining lollawing results: aeronautthen measuros ine Adundance Mass Isotcpa Mellaeaa#4Mg 78 &8 ~Mg 10,0023 90aAC1101259Ennithtatomic ml9smlgna sium Ior thg phnc? declmal placos und Includa the approprlatc WnitaEIPTGET YounanowerMew Avallable Hlnt(a)ValueUmitsEMe
external tool Available after Sep at 11.59pm 20 0f 21 Roviow | Constants | Penodic Table abuntanco Uragnesium on Iha newidnel colaining lollawing results: aeronautthen measuros ine Adundance Mass Isotcpa Mellaeaa #4Mg 78 &8 ~Mg 10,00 23 90 aAC 1101 259E nnithtatomic ml9s mlgna sium Ior thg phnc?...
##### Give an example of:An indefinite integral involving a square root that can be evaluated by first completing a square.
Give an example of: An indefinite integral involving a square root that can be evaluated by first completing a square....
##### 6.y = Vx - 1 7. 1 = %2 + 3 8. I = ly + 2 9.y = 21 10.y = 23+3
6.y = Vx - 1 7. 1 = %2 + 3 8. I = ly + 2 9.y = 21 10.y = 23+3...