Calculate the given quantity if u = i +j- 4k v = 5i – 2j + k w = j- 3k. (a) 2u + 3v (b) |u| (c) u v

Q: Which is NOT a solution of V2- i ? C. -0.4717 + 1.2196i D. -0.8204 – 1.0183i A. 2.2094 0.3442i B.…

A: To find the nth root of a complex number we have to use de'Moivre's formula :…

Q: What is the general solution of - 19 + 30 = 0 ? dt Oy = Ce + Cze + C3 cos v5 z + C4 sin 5z Oy =…

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Q: 3. Find the general solution for y" – 10y' + 25y = 0 s.t y(0) = 1, y(1) = 0

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Q: use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

A: Given the relation 30=3x+2y. We need to minimize the value of U = (x+3)(y+5). Substitute the value…

Q: Exercise 3. compare the values of dy and Ay in each case (3a) y = 0.5r" I = 2 Ar = dr = 0.1 (3b) y =…

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Q: FIND THE GENERAL SOLUTION! *SOLVE FOR U? Uyy + Uy = 0 WHEN Y=O U = f(x) Uy = g(x)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve the Dirichlet problem on {x² + y² < 1} | u(x, y) = 2xy + 2y² on {x² + y? = 1} Au = 0 %3D

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Q: (b) Use Gaussian elimination to find the values of x, y and z: x+2y+3z=10 -x+y+z=0 y=z=1

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Q: This is the solution of y" + 3y' + 2y = 8 (t – 1), y (0) = 0, y' (0 O y = [e+-e "]U (t – 1) O y = [e…

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Q: 3. Find the general solutions of, (xy + x* )dy + y°dx = 0 b.

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Q: Solve the fallowing Cauchy problem U4- Au + cu=0 in R" x(0, 0) On IR"x{t=0}. U = where c is a…

A: Given the Cauchy problem as ut-∆u+cu=0,             in ℝn×0,∞                (1) re-write the…

Q: дz For z = x² + xy³; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 dv

A: Let's solve given derivative functions.

Q: What is general solution of v = ds/dt if v = 2/t^3/2? a.-4/t^1/2 = s^2 + c b.-4/t^1/2 = s + c^2…

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Q: 1. (3x – 2y + 1) dx + (3x- 2y +3) dy = 0, %3D Ans. 5(x + y+ c) = 2 In | 15x - 10y + 11L

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Q: Minimize c = r + 2s + 3t 3r + 2s + t > 60 Subject To: 2r + 3t > 60 And Where: {r > 0, s > 0, t > 0}…

A: According to the given information it is required to solve the given problem:

Q: What is the general solution? d3x d?x – 4x = 0 dt3 dt2

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Q: ) The general solution of (G) is: V2 a. u(x, t) etwr w2 |dw. 27 +*[1+ w°e¬w*«j]dw. - w²/2n b. u(x,…

A: The answer for part (5) is C.

Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

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Q: Determine the general solution of (s +t?) ds +st dt = 0. 82+2t2 O+2s2 %3D = C O s4 +2s2t2 = C

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Q: 2. Solve the I.V.P. (4у + 2t - 5) dt + (6у + 4t — 1) dy 3D 0;B у(-1) — 2

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Q: The solution of the IVP x dx + 2ydy30, y(0)=2 is O None of these. x3 4- y3D x3 y=21 3. y=2,1+

A: Variable separable form : If the variable of the differential equation is separated then; Rewrite…

Q: Find the solution of z'y" + bay + (4 + 4r)y - 0, z > 0 of the form where co 1 Enter n1,2,3,...

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Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

Q: Use your finding(s) in part (2) to demonstrate that the simultaneous system of nonlinear equations…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the general solution of this ODE: d²y dy + 7. + 10y = 3t2 + 4t – 1 dt? dt

A: We have to solve the given differential equation.

Q: (T^2-x)dt-tdx =0 when t=1 x=5 Ans,: x=1/3t^2 + 14/3t please show solution

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Q: 1. Find the solution of the IVP. Show the details of your work. y" + 5y' + 6y= u(t − 1) + d(t − 2),…

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Q: dx dt dy x - 7y? || dt ||

A: In order to find critical points we equate both the equations to zero

Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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Q: 4(a)Verify that the equation y = Inx – Iny is an implicit solution of the TVP, ydx = x(y+ 1)dy y(e)…

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Q: Solve the equation (y+ u)Ux+yuy = x -y with the initial conditions u(x, 1) = 1+ x. %3D

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Q: 3. Find the general solutions of, dy _ x+ y dx х-у, a.

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Q: Verify that u(z, t) = f(e'r) solves the initial value problem (a,u + z8,u = 0, u(x,0) = f(x).

A: Take the partial derivatives of u(x,t).

Q: Find the solution of Uy = 36 ut + 10 u if Ux U₂ (x,0) = 3e-2t using the method of separation of…

A: Given partial differential equation is ux=36ut+10u____(1) and given condition isux(x,0)=3e-2x We…

Q: D.Linear Homogeneous DE with Constant Coefficients: 2. (D2 – 2D – 3)y = 0 ; x = 0; y = 0; y' = -4

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Q: This is the solution of y" + 4y' + 3y = 8 (t – 2) , y (0) = 0, y' (0) = 0 O y = [e-t-2) –e-8(t-2)] U…

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Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: Determine the particular solution. v" – 2y' + 5y = 0; v(n) = 1,v'(n) = 0 Oy- e(0.04cos(2x) -…

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Q: What is the most appropriate substitution equation in order to solve the equation…

A: The given differential equation is -  (x+2y-1)dx+3(x+2y)dy=0 Rewriting the above equation as  -…

Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

A: The given equation is  x2y"-xy'+x2-24y=0                                  (1) The differential…

Q: The solution of D.E (x – 1)²y" + 8(x – 1)y' + 12y=0,x#1 Select one: O a. v(x) = c,\x|-3…

A: The differential equation is x-12y''+8x-1y'+12y=0.

Q: 3. Find the general solution of dy = y(xy – 1). d:r

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Q: 3. Using the general solution: x(1) = A1cos(@nt) +A2sin(@t) Calculate the values of A1 , A2 in terms…

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Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…

Q: 3)6x+Tg?t3zニ202%さ-14yこ 8エzIAns. -37 A ns: Positive semi definite ] 87xT

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Q: Solve the second-order DE y"+2y'+4y= g(1), y(0)= 0, y'(0)=1, where 2, Ost<2 g(1) ={-2, 2si<4 0, 124.

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Q: Find the general solution of (D4+50D²+ 625) y=0 A y=c,cos5x+c „sin5x y=c,cos5x+c,sin5x + c zxcos5x+c…

A: Answer: option C is correct answer To find: general solution.

Q: = 1 on the domain a² < x² + y² < b², Question 3. Solve the equation uxx + Uy with u vanishing on…

A: Consider the given equation: on the domain with u vanishing on both the boundaries