In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
4.
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- 2. U = Uxx OLALA u(dt)=ula, t) = ( ula, 01=0 4t=(2,0) sin a t 70arrow_forwardSolve Laplace's equation, = 0,0arrow_forward4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y" = 0 on (-0o, 00).arrow_forward1. Find all singular and all ordinary points of the DE (0.5x²+2x+25)y"+xy'+y=0arrow_forward2) 3 3 dr+du+ +y=t dr subject to x = 1 and y = 0 at t = 0arrow_forwardProblem 1. Let f(x, y, z) = ln(² | y² | 2²). a) What is the direction of maximal increase of f at the point (1, 1, 1)? b) At the point (1, 1, 1), how far in the direction found in (a) do you need. to go to obtain an increase of 0.1 in /? c) At the point (1, 1, 1), how far in the direction of (1, 1, 2) do you need. to go to obtain an increase of 0.2 in /?arrow_forwardQUESTION 3 31 in the diagram befow line seument AB mtersects ine egnt OC and a the size of r ond y (4) (a) DCE (3) (b) 150 20 120 (c) Zx-20 80 (d) Find the values of x, y and z if Ab//Cd. 120arrow_forward7. Integrate. Sad" √1-(x-1)² x+y x² + y² dydxarrow_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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