2 2 22 if== prove that 22 a¯x +b¯y¯ +c¯=¯ 3, ,3, 3 a'x + b°y +c°z xyz abc %3D

Q: 1. Given w = x²y³z+x*yz³, x = cos(4t),y = sin(5t),z = In(t). Write the tree diagram for . Then,…

A: NOTE: The equations provided in the bottom part of the question do not match with the equations you…

Q: Q.5 Solve the BVP V²u = uzz + Uyy = 2, Uz (0, y) = uy(47, y) = 0, u(x, 0) = 0, U(x, 7) = 2 sin () 0…

A: Given equation is  ∇2u=2 , 0<x<4π , 0<y<πux0,y=uy4π,y=0uxx,0=uyx,π=2sinx4 Now, let the…

Q: find c, and c2 so that y(x) = c1 sin x+ c2 cos x will satisfy the given conditions. Determine…

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Q: 1. (a) Find dy/dx for y = 1 + (x² – 1)(x³ – x) without first expanding the bracket. | 1+ u (b) Find…

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Q: 14) Find the general solution of y" + 6y" + y' – 34y = 0 if it is known that y, -4x COs x is one = e…

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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: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Solve the Neumann problem Ди — 0 Uz(0, y) = 0, Uz(7, y) = D, cos(ny) Uy(x, 0) = 0, u,(x, T) = 0 0 <…

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Q: 2. Find the solution u = u(x, y, t) of the following initial value problen Un + yu, + 4xuy = -u²,…

A: We solve this equation by Partial differentiation method: The given equation is ut+yux+4xuy=-u2 We…

Q: 10. On C[0, 1] defiue S andT by y(s) =s x(t) dt, y(s) = sx(s), %3D respectively. Do S and T commute?…

A: We have: S,T:C[0,1],∥.∥∞→C[0,1],∥.∥∞ are defined as S(x)(s) = s∫01x(t) dt  and T(x)(s)=sx(s)…

Q: Dear Sir,   Please can you slove this equation. Partial derivative.

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Q: S Ive the Neumann problem { 0 < x, Y < 0 < y < T 0 < x < T || cos(ny) Uz(0, y) = 0, Uz(7, y) = E1…

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Q: 2 1. The cissoids y : %D а —х

A: Given the equation  of cissoids y2=x3a-x As per our guideline we are supposed to answer only the…

Q: (d) Using the method of characteristics, or otherwise, find the general solution to yu, – x*u, = 0,…

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Q: 2 2 X = {K_EW : S" (Lu' (+)/² + 9 ª 14(+)1³)dt< =0} O why this is inner Product ?

A: Given: X=u∈W:∫0∞u't2+92ut2dt&lt;+∞   To explain: Why the given condition represents an inner…

Q: a) The propagation of a wave u(x, t) in a long cable is described by the following initial value…

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Q: #3. Solve the following Cauchy problem: 2 Ou + cu = 0 - u = g where c is a constant. in /R" x(0,0)…

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Q: 9. z = xe-; P(1,0, 1) 10. z = In /x² + y²; P(-1,0, 0) 11. z = e³y sin 3x; P(7/6,0, 1) 12. z = x/2 +…

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Q: 3. Using integration by parts (IBP), what should you pick for u and du in 5z cos(3r) dr? = cos(3r),…

A: Integration By Parts formula is used for integrating the product of two functions. This method is…

Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: 3. Use Green's Theorem to evaluate (y-6y) dr + y + 10y) dy where Cis shown below y (-11) (1-2)

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Q: Evaluate: S ndy 2y+3 (y 1)(y 1) In G) ny² + y + 1| - arct arctan 0 Inly 1| ž(y 1)* nVi y arctan( ) c…

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Q: 12. Let z = æ²y – xy²,x = e " ,y = e#, then which of the following is ? %3D at O a. -2et – 2e-2t O…

A: Partial differentiation of a function is the derivative of the function with respect to one variable…

Q: 1. The loop of y² = x * (4 - x) 2. у %3D 6х — х?, y = x² – 2x - 3. у %3D 2х y2 + 4x – 8 = 0 - 4. An…

A: Question 4 : Arch of y = (1/3)sin(x/3) First find out intersection points :  y = 0 (1/3)sin(x/3) = 0…

Q: 5 Qu/ If w=f(u, v) = cos uv, u = xyz , v = 4(x²+y²) dw Prove that 0 at the this point…

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Q: Given that y, =sin(2 x) and y,=cos(2 x) are solutions to %3D y"+p(x) y' + q(x) y =0. Let y,= v, Y,+…

A: v1 is given by -∫y2gxWxdx Here g(x) = 3x, y2= cos2x Calculate the Wronskian and put these values in…

Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: Which of the initial value problems below are guaranteed a unique solution by the hypotheses of…

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Q: 5. Use the energy method to prove the uniqueness of the solution for the problem 0 0 t> 0 U = kurg +…

A: Given : ut=kuxx+hx,t0&lt;x&lt;L,…

Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

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Q: and c(r) is the unique solution to y" + y = 0 : y(0) = 1, y'(0) = 0 %3D to prove that c(r+ y) =…

A: Given- c(x) is unique solution to- y''+ y =0 : y(0)=1 , y'(0)=0 To prove that- c(x+ y…

Q: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

Q: 1. Given tha y=c,e** +c,e* is a two -parameter family of solutions of y" – 3y' – 4y = 0 on (-0,00),…

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Q: dy 1. If (x + y)² = x² + y² prove that 11 I Alx y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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: Find a solution for the given Cauchy Euler equation for t>0   (t^2)z''+27tz'+169z=0

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Q: find c, and c2 so that y(x) = c, sin x+ c2 cos x will satisfy the given conditions. Determine…

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Q: 1. y = Ax² + Bex 2. y = C₁ ex cos3x + C₂ ex sin3x 3. y C₁e* + C₂e²x + x 4. Iny = C₁e* + С₂е¯* 5. x =…

A: As you have asked multiple questions so that I have answered first question as per the guidelines.

Q: 6. Solve Pu ay au = 0 for 0<x< 1, 0<y<1, u(x, 0) = (1 – x)², и(х, 1) %3D 0, %3D du (0, y) = 0, ax и…

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Q: Y Z H K Given: YX = HX, mZY=mZH, MZZXY=mZKXH Prove: YZ = HK er: AZXY = A by reason

A: Using , Angle - side - angle test,

Q: 3. Find the general solution of xy' = x – y + xytanx a. xycos x = xsin x + cos x +C b. ycos x = xsin…

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Q: The indicated Turi Is a solution of th1e given d merentiai equation. Ose iula (5) Tn Section 4.2…

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Q: 2 I| ysin(xy)dydx Н.W.

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Q: Example 1.4: Is y(x)= c, sin 2x + C2 cos 2.x, where trary constants, a solution of y" +4y = 0? and…

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Q: 3. Show that the solution of the equation 28 bonicido at ƏT PT satisfying the conditions: g pc…

A: Given, ∂T∂t=∂2T∂x2  T(x,0)=xT(0,t)=T(a,t)=0 Consider the solution be T(x,t)=X(x)T(t)        ...(1)…

Q: 7. Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1 8. Solve the following…

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Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y, y(0) = 1. %3D

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