Suppose trat a fourth order oterentur equaton has a solution y Se sin(z) a) Find sucha dferenmal equation, assumingtis homogeneous and has constant coemcients hep equations (b) Fina the general sonon tohs anerennal equation in your answer use c. and to dencte artitrary constants and z the independent varabie Enter as ct. as ca. e hep (equations)

Q: The general solution of y" + 16y = cost is: Select one: a. y = C,cos(4t) + C2sin(4t) + cost 15 O b.…

A: A detailed solution is given below.

Q: 5) Find tue soletion of the differen tiel equation dr Sec't which paffes dt fant +1 turough the…

A: Solve the differential equation by separation of variables.

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

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Q: 1 - / sin2r - ycos2r điferansiyel denkleminin genel çöztumt aşağıdakilerden hangisidir? a) Hiçbiri…

A: Consider the homogeneous differential equation y'sin2x-ycos2x=0. Variable separable form:…

Q: 2 Solve this Di fferential equat ion by applying ( variation paramet ers) 4+y = y+y%3DSE c x

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Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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Q: When a particle is located a distance meters from the origin,a force of Cos(πx/3) newtons acts on…

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Q: Consider the mass-spring system for mass 2.5 kg, spring constant 2.2 N/m, and an oscillating force…

A: In this question we are given with a equation which is a differential equation and we have to find…

Q: The general solution of y" + 16y= cost is: Select one: a. y = C₁cos(4t) + C₂sin(4t)--1/17tcost…

A: We have to choose the correct answer from the given condition according to the given condition

Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

Q: [3] Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the motion is…

A: Given equation is, my''+by'+ky=0 So, the auxiliary equation of the given equation is,…

Q: Q find Soluti on Of ion or me Vibrating equati Violin Shing azucxit) 6² Q?U (xit 1) 2. 2. which has…

A: Given an initial value problem, ∂2ux,t∂t2=c2∂2ux,t∂x2 With boundary conditions, u0,t=0 and uL,t=0.…

Q: A flexible string of length t is tightly stretched between x = 0,x = n, on x-axis, its ends being…

A: To solve the problem we use the method of Laplace transformation also Laplace inverse transformation…

Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

A:

Q: Let u and uz be two solutions of the nonhomogeneous equation Ly] = y" + +y= sin(t). Then y = u - uz…

A: There is a theorem that which I am stating below:

Q: Which of the following could be a linear homogeneous differentia equation (with the smallest order…

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Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: Hiw/ If isinh Z= siniz, proveThat: sinhz= sinhxcosy +ising cosh x

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Show that xo = 0 is a regular singular point of the equation xy" – 5 - +x ) y' + 3y = 0). Determine…

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Q: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: 2- Verify the following identities : [Sinh( u+ v)+ Sinh(u-vl a) Sinhu.Coshv = Coshu.Cosky =-…

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Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: The second-order difference equation Yk+2 - 3yk+1 + 2yk = 2 sin(3k) (4.164) has the homogeneous…

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Q: Solve for the particular solution of the following non-homogeneous DE. y” – y’ = 2sin 2x

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Q: Y= JB cos(5x) + sin (Sx) ナ0<X6 1.) Local Maximun pointo) are [? 2) Lecal Minimum point(3) pointis)…

A: Given that  Y = √3Cos(5x) + Sin(5x).  To find , Local Maxima and minima , Absolute maximum and…

Q: The homogeneous equation with constant coefficients of least order that has y = 2e3t + 3 sin(3t) +…

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Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: 1. The limaçon x = 2 cos t – cos 2t, y = 2 sin t, 0 <t < 2m find area y

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Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

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Q: 2. %3D be Centered in a batt co,ogo) andradies I 2. frove thet S-273R

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Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

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Q: Show that xo 0 is a regular singular point of the equation %3D xy" + + x ) y' – 4y = 0. Determine…

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Q: Verify if zo = 0 is a removable singularity for sinh z (ii) sin z3 (i) z2 (ii) 2³e/=, Explanations…

A: A limit is a mathematical object perceived to represent the last object in a sequence of the same…

Q: The first condition allows computation of the spring constant, k. It follows that the damped…

A: we will first open the complementary solution associated with homogeneous part of the equation then…

Q: The non-homogenous solution of the following equation by using variation of parameter method y" + y…

A: Given

Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: Suppose that y1=e^x and y2=e−x are two solutions of a homogeneous linear equations. Explain why…

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Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: 1) LtZ be a solukion (5) of complese mumber then the sinh Z+ Coah z -e is Z=1?

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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.