Q.6 Solve the Laplace equation U+U = 0 U (0,y)=0,U,(z,y) = 0, U(x,0)=2cos3x+3-2sin²x U(x,1)= cos²x-¹+cos4.x, Hint: U(x, y) = a +by+Σ(A, coshny + B sinh ny) cos nx.

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (6 e'V5) i+…

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Q: a) Which of the following systems of ODES is autonomous and dynamical? where ty₁ = e-sin(₂), y₂ = ₁…

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Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

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Q: Express a general solution to 2x(1 – x)y" + (3 – 10x)y' – 6y = 0 Using Gaussian hypergeometric…

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Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: The equations re + uz – cos(v) – 2 = 0 and u cos(y) + 9x?v – 3yz² – 1= 0 can be solved for (u,v) as…

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Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: y' t (oy - a sn 8t y W): -I

A: Given the differential equation is y'' + 16y = 2 sin8t,   y0=-12,   y'0=0

Q: a) Find the total differential for the following function z = f(x,y) = xy + y xb) Use Chain Rule for…

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Q: Let u = u(x, t), x, t ≤ R. Solve Ut + 5ux + u = 0 u(x, 1) = = COS X

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Q: DATE Find the differential of the given function. ose the best answer a) dy: -x) dx xp (x-1)

A: here option B is true

Q: a) Find the relationship between Ju(x) cnd je(x) by comparing the invariont forms of [x;, x, x- r?]…

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Q: use Laplace trans forms g - 4 y + g'co)= o 3 y = 6t - 8 , ylo)=0 ,

A: Solve the following

Q: Given z=4x² + y2 -2 and C: x=cos t, y= sin t for [0,2] a) Find z'(t) using chain rule (not…

A: ### Part (a): Finding  z'(t)  using the chain ruleGiven the function  z=4x2+y2−2  and the curve  C…

Q: dz Use chain rule to find at (u, v) = (1, 1) if dv z = z sin(y² – z + 1)4), e = 3u – v², y = vº.

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Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

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Q: (x²+y2 ) prove ne du + y ax -2 sin2u ( Euler's Rule) 5. If u = cot-1 that x ду x+y

A: We use the Euler's rule of partial differential in homogeneous function to solve this problem.

Q: QI/ Study the Cauchy -Riemann equations and determine this equation satisfy it or not. f(z) = e =…

A: Given that: f(z)=ez=ex[cosy+isiny]

Q: How do I solve the laplace(u(t-2)cos(t-2))

A: The Laplace transform formula for translation on the t-axis is given by ℒ{u(t-a) f(t-a)} = e-asF(s),…

Q: Ã(x, y.z)=(4xy²-x')i+(2e"-ycos2xj+(x'siny k . and Əyəx Əx' əy² 'Əxôy Find:

A: Given -  A→(x,y,z) = (4xy2-x5)i^ + (2exy-ycos2x)j^ + (x3siny)k^We have to find the following -…

Q: 1. y = 5u°; u=7x – 4x' + 2x –9 2х-9 u +1. u=Vx? +1 y = u? -1' 3. x=7y -3y +y +8 2.

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Q: The equations re + uz – cos(v) – 2 = 0 and u cos(y) + 4r?v – 5yz2 – 1 = 0 can be solved for (u,v) as…

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Q: (7) Show that the given functionis an integrationy factory Solves a) Sinydx+ Cosydy =0(e),…

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Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: laplace(u(t-2)sin(t-2) )

A: laplace(u(t-2)sin(t-2) ) = e-2ss2+1

Q: Let w = x³y cos(5z). Find the following. (a) g(x, y, z) = дw (b) Əy(x, y, z) = ду (c) o (x, y, z)…

A: Given data÷

Q: Find the zeros of Q(x) = 5x - x² + 9 using the quadratic formula. Number of zeros: one

A: Given Quadratic formula is Q(x)=-x2+5x+9 Compare to ax2+bx+c=0 Here a=-1, b=5 and c=9.