3. Solve of the Boundary-Value Problem (BVP) by the method of seperation of variables.диat9mxu,(0,t) = 0, u(2, t) = 0, u(x,0) = 8cos 6cosSHAN(d) u = 8e-9m²t/16 cos3Txsin 5x6e-81m³t/16 cos3mx4-The answer97x4

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Answered: 3. Solve of the Boundary-Value Problem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 13. Let a,b be constants, a 0. If Y = aX+b, show that P(X, Y) = lifa > 0 = -1 if a < 0 P(X, Y)
2. Suppose that y₁ is a solution for of the homogeneous SOLDE " + p(t)y' + q(t)y = 0. (a) Explain how to find a non constant function tv(t) such that y2(t) = v(t)y₁(t) is also a solution. (b) Explain why y₁ and y₂ are linearly independent.
Let a be a constant and f(x, y) = x – 3axy + y°. Determine that the following statements are "True" or "False". Türkçe: (f(x, y) = x - 3ary + y ve a bir sabit olmak üzere aşağıdaki ifadelerin "Doğru" veya "Yanlış" olduğunu belirleyiniz. ) 1. f(x, y) has a local minimum value at (a, a) for a > 0. (Türkçe: f(x, y) fonksiyonu a > 0 için (a, a)'da yerel minimuma sahiptir.) 2. f(x, y) has a local minimum value at (a, a) for a 0. (Türkçe: f(x, y) fonksiyonu a > 0 için (a, a)'da yerel maksimum sahiptir.) 5. f(x, y) has a saddle point at (0, 0) when a = 0. (Türkçe: a = 0 iken f(x, y). (0,0)'da eyer noktasına sahiptir.) 6. f(x, y) has a saddle point at (0, 0) for a > 0. (Türkçe: a > 0 için f(x, y). (0,0)'da eyer noktasına sahiptir.) 7. f(x, y) has not a saddle point at (0,0) when a = 0. (Türkçe: a = 0 iken f(x, y). (0, 0)'da eyer noktasına sahip değildir.) 8. f(x, y) has not a saddle point at (0,0) for a > 0. (Türkçe: a > 0 için f(x, y), (0,0)'da eyer noktasına sahip değildir.)
The number of defects on the front side (X) of a wooden panel and the number of defectsa on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy(x,y)=c(x+y), x= 1,2,3 and y=1,2,3. Determine the value of c.
(1)If A = (xy², yz³, Find grad(divA)
b) The utility U(x,y) units of satisfaction form owning x units of commodity 1 and y units of commodity 2 is given by U (x, y) = 2xy + 8x + 3y + 15 %3D units per day. Currently 27 units of commodity 1 and 12 units of commodity 2 are consumed. Use Calculus to estimate the change in utility if he adds 2 units of commodity 1 and removes 3 units of commodity 2.

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3. Solve of the Boundary-Value Problem (BVP) by the method of seperation of variables. du at a²u 3mx u,(0,t) = 0, u(2,t) = 0, u(x,0) = 8cos - 6cos 9mx