In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
5.
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- Solve Laplace's equation, = 0,0arrow_forwardThe equations ry² + 6xzcos(u) + ye" = x'yz + xe" – 7u?v² = 21 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (5,0). Find ()zy at P. 12 and %3| 12,00 -70,00 -30,00 -0,17 56,00arrow_forward1. Find all singular and all ordinary points of the DE (0.5x²+2x+25)y"+xy'+y=0arrow_forward2. U = Uxx OLALA u(dt)=ula, t) = ( ula, 01=0 4t=(2,0) sin a t 70arrow_forward3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions du (г.0) 3 0 r,-|=0, 3 u(1,0) = sin(20) du r,-|=0 3 u(1,0) = sin(20) (r,0)=0 +arrow_forward4. An imaginary ant is walking on an imaginary cartesian plane so that at any point (x, y) it moves in the direction of maximum temperature increase. If the temperature at any point (x, y) is T(x, y) = -e2y cos x, find an equation of the form y = f(x) for the path of the ant if it was originally located at (T/4,0).arrow_forwardWhich of the following is NOT a possible solution for Laplace's equation? (a) y = (AePx + Be-P*)(Ccos py + Dsin py) (b) y = (Acos px + Bsin px)(CEPY + De PY) (c) y = (Ax + B)(Cy + D) (d) y = (A P* + Be-P*)(CePy + Depy) O a O b O carrow_forward1. Solve Laplace's equation inside a rectangle 0 0 and H > 0), with the following boundary conditions: a) u(0, y) = g(y), u(L, y) = 0, (r, 0) = 0, and u(x, H) = 0. b) u(0, y) = g(y), u(L, y) = 0, (x,0) = 0, and (x, H) = 0.arrow_forwardEx. 5.2. Find the deflection of a rectangular membrane with sides a and b with c² = 1 for the initial deflection f(x, y) = sin 3πx a sin 4πy barrow_forward- 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) + v cos(0).arrow_forward4. Determine when the following pairs of functions are linearly independent. (a) yı(t) = erit; y(t) = er²t, r₁,72 € R (b) y(t) = cos(at); 32(t) = sin(at), a = R (c) y₁ (t) = cosh(at); y₂(t) = sinh(at), a € Rarrow_forward15 Find ( T + In y) dydxarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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