Solve the Laplace equation subject to the boundary conditions, u,(0, y)= 0, u(2, y) = 0, u, (x, 0) = 0, u(x, 2) = x(1 + cos(nx/2)), for 0

Q: 7 Calculate § (-y³dx + x³dy) where 2 Y ² + y ² = 4 by using Green's theorem C -Z 2 F² = (cosz +…

A: As in Green's theorem we can change line integral into surface integral,i.e.

Q: Show that u(x, y) = e* cos y + 2e* sin y + e* cos y + 2e* sin y satisfies the equation ²² + ax² dy²…

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Q: (1+x²) uz + Uy = 0, u(1, y) = sec y

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Determine the Laplace transform of e-5t sinh(6t) · е s+5 s2 – 10s–11 6. s2 – 10s-11 s+5 10

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Q: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

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Q: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

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Q: (3) If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

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Q: Find a solution of x dy = y²-y that passes through the indicated points. dx (a) (0, 1) y = (b) y = 1…

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Q: Hiw 2 Find dy For (πCシ)

A: Differentiation of the function helps to find the derivative of the function. Simplification of the…

Q: What is the minimum value of y = 3 + cos 2x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: 12. Evaluate c Vx² + y² ds_along the curve r(f) = (4 cos t)i + (4 sin t)j + 3tk, –27 < t < 27.

A: According to the given information, it is required to evaluate the integral over the given curve.

Q: Solve for the higher order DE number 2

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Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = &lt;2, 5, 1&gt; and initial…

Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

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Q: Let h(x, y) = x5 + y sin²x x² + y² 0, { 25 if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: h(x, y) = cos(7x + 13y) Find k such that h(x, y) = k has no solutions. Show that h(x, y) = 1 is a…

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Q: a) Find dy if y² + x²y² = 1+x^y use implicit differentiation b) If x² + y² = 6. Find y' in term OF…

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Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: Set w(r, y) = cos(xy) where x = t² and y = el-8t, then dw dt Select one: a.…

A: to find the value dw/dt                   dwdt=dwdx.dxdt+dwdy.dydt                     (1)

Q: Salve 6y"o)-5y'Lx)+Yx)= esinx+ cos2X with

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