In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
7.
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- 2. U = Uxx OLALA u(dt)=ula, t) = ( ula, 01=0 4t=(2,0) sin a t 70arrow_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_forward15 Find ( T + In y) dydxarrow_forward
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- 7. Integrate. Sad" √1-(x-1)² x+y x² + y² dydxarrow_forward5. The function r(t) moving in 3D space. = (2 sin (¹), 3, 2 cos (t)) parametrizes (draws) the path of a particle (a) Evaluate r(t) at t = 0, 1, 2, 3, 4.arrow_forward24. Show that Legendre's equation (1-x²)y" - 2xy - λy=0 is self-adjoint.arrow_forward
- 4. 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_forward17. Evaluate the line integral xe dx +y sin y dy along the triangular path consisting of the line segment from (0,0) to (2,3) followed by the line segment from (2,3) to (1,0) followed by the line segment from to (0,0). (1,0) a. 0 е. 8 3 b. 25 f. 25 9 c. 26 g. 26 9 9 d. 3 h. -3arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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