11. Determine the solution of Utt = u (x,0) = 0, u (0, t) = h, where h, k, and A are constants. c²ur + Asinh xa, ut (x,0) = 0, u (l,t) = k, 0 < x < 1, 0≤x≤l, 1, t> 0, t> 0,

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Q: Let f(x, y) = 3x²y + y³ - 3x² - 3y² + 2. Find all the critical points.

A: fx, y=3x2y+y3-3x2-3y2+2 We have to find all critical points of the given function.

Q: The equations xy² + 8xzcos(u) + ye" = 16 and xyz + xev – 9u?v² = 27 are solved for u and v as…

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Q: Let F(x, y, z) = x3³yz² - 6x²yz + 9xz - 2y³z. Find F Fxyz' 3x²yz² - 12xyz +9z+ x³z² − 6x²z − 6y²z +…

A: This question is based on Partial Derivative.

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

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Q: Suppose that a consumer derives his utility from two goods, the amounts of which are x and y,…

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Q: xy* Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (a4+6y8)

A:

Q: The equations ry? + 5xzcos(u) + ye" = 10 and x³yz + xe" – 10u2v² = 30 are solved for u and v as…

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Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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A:

Q: 31 Xi + 47 Xz + 14X3 Ex Al+

A: Given: Max z=31x1+47x2+14 x3Subject to; 2x1+3x2+x3≤4 and x1, x2, x3≥0 To find: Optimal solution and…

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

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Q: 5) y = V V+ V? + Væ

A: The function: y=x+x2+x

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A: Given equation is  ax+b2y"+aax+by'-a2b2y=ax+b1b Cauchy Euler equation . To solve this put…

Q: The equations xy2 + 6xzcos(u) + ye" = 12 and x³yz + xe" - 8u²v² = 24 are solved for u and v as…

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

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Q: ts) Find two linearly independent solutions of 2x²y" - xy + (2x + 1)y=0, x > 0 e form - 1/1

A: for the differential equation 2x2y''-xy'+(2x+1)y=0,x&gt;0 To find the ser

Q: Calculate az/ax, where xez + zeY = x + y.

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Q: r(2,4) Sa (2y+x) dx +(3x– y)dy} along the straight line x-2t and Evaluate J(0,3) y=P+3.

A: