2. (Theorem 2.1, Eq. 2.5) By employing change of variables r = ax +y and s= bx +y, prove that the PDE: A Urr + Bury + С Uyy has the following general solution: when: = :0 u(x, y) = F(ax + y) +G(bx + y) A ‡0, B²-4AC #0

Q: Form 2 of the chain rule. Do the following problems: A. Let z = u² + v²; u = 2x + 7, v = 3x + y.…

A: To apply chain rule for this problem, we first need to identify the composite functions involved.…

Q: (x, y) = (b) 1 1 (d) 1/2 Does not exist. (x, y) = Ty³ x² + y6 = Find limf(x,y) along the path x =…

A: We will find the required.

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A: Note: In the given problem  is given so taking it

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A: "Since we are entitled to answer up to 3 sub-parts, we will answer the first three  as you have not…

Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

Q: If f(r, v)= +y-2y, find fa (2, 1), f (2, 1), fay(2, 1) and fy(2, 1).

A: Given a function f(x,y)= x3+x2y3-2y2 Now, fxx= ∂2f∂x2=∂∂x∂f∂x fyy= ∂2f∂y2=∂∂y∂f∂y…

Q: 2 4 2) f(x,y)=2xy- 5x? - 2y² +4x+4y – 4 Ans. f 3'3 0 local max. %3D

A:

Q: Compute u x v. (a) u =i-j+ 2k, v = 3i +j+2k (b) u = 2i + j – 2k, v = i+3k (c) u = 2j + k, v = 3u 4…

A: To compute: u×v. If we have two vectors A=x1i+y1j+z1k and B=x2i+y2j+z2k then: A×B=ijkx1y1z1x2y2z2…

Q: Which of the following functions V(y1; Y2) is a Lyapunov function for the dynamical system y1 =…

A:

Q: rks) Find the solution of the following problem: Utt = 9uzz, x > 0, u(x, 0) = x², u(x, 0) = 6x +3,…

A:

Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: s2+2 s+1 S s+1 52–2s (4) s(s²+4) s+2s (2) s2+2 (3) s2+2 (5) (1) input=x(t) output=y(t) diferantial…

A: Find the explanation below

Q: (c) Consider the double integral || xy dA where D is bounded by the x-axis and the upper half…

A:

Q: 7. Which of the following is the potential function for F = (2ху + 1,х2 + 2yz, y? — 2)? а. Ф(х, у,…

A:

Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

A:

Q: The equations xy² + 8xzcos(u) + ye" = 16 and x³yz+xe" – 3u?v² = 9 are solved %3D for u and v as…

A:

Q: Which of the following functions V(y1, Y2) is a Lyapunov function for the dynamical system y1 =…

A:

Q: )Please answer in legible and clear handwriting.

A: Given that  xn,xn-1,....,xn-i be a sequence of successive approximation vectors to the solution of…

Q: 79. Two dependent variables Express v, in terms of u and v if the equations x = v In u and y = u In…

A:

Q: The equations xcos(u) + luy² + e² + 2 = 0 and 9ye" + 4x²v – 3xcos(z) +1=0 are solved for u and v as…

A:

Q: 9. Find the direction of zero change for the following function at given point (Баллов: 2) xy + y,…

A:

Q: 2. Let f(x, y) = 4x³y² + 3x²y³, find: (a) Vj (1,2) (b) f(1,2), where u = 17-17

A: (2)  Given that  f x, y = 4x3y2 + 3x2y3  (a)     ∂f∂x = 4y2∂∂xx3 + 3y3∂∂xx2       ⇒ ∂f∂x = 4y23x2 +…

Q: The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x,…

A: Consider the given information. utt=uxx                 -∞<x<∞t>0ux,0=2xutx,0=e-x D…

Q: y =c,J,(x) +c_Y, (x) .A y=c,J,(x) +c,Y, (y) .B y=c,,(x)+c_y,(x) .C y=c,J,(y) +c_Yn(x)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The equations ry?+ 5zzcos(u) + ye" = 10 and r*yz+xe" – 10u²v² = 30 are solved for u and v as…

A:

Q: Decide whether it is possible to solve the equations xu? + yzv + x²z .xyv³ + 2zu -- u?v² = 2 for (u,…

A: 3.7 Given equations are xu2+yzv+x2z=3xyv3+2zu-u2v2=2 The points are  (x, y, z)≈(1, 1, 1) and  (u,…

Q: In the xy-plane, new coordinates s and t are defined by = ¹/(x + y), t = 1/(x −y). Transform the…

A: