In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
9.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
- 9. Form the differential equation of the three-parameter family of conics y = ae* + be2x + ce¬3x where a, b and c are arbitrary constants.arrow_forward4. Find the velocity and acceleration of a particle whose position function is x(t)=sin(2t)+ cos(t)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_forward
- - Problem 5: A particle moves along a line with a velocity given by v(t) = t² – 2t where v is measured in meters per second. Find the displacement of the particle as well as the total distance traveled for 0 ≤t≤3.arrow_forwardEx. 5. Find a solution of Laplace's equation, u +u„ =0, inside a rectangle subject to the following boundary conditions: а. и(0, у) 3 0, и(, у) 3 0, и(х,0) — -4sin (2rx). и(х,5) %3 6sin (3rx). b. и(0), у) - 0, и(, у) - 0, и(х,0) —х', и(x,2) -0. с. и, (0, у) 3 5sin (ту). и,(1, у)-13sin (2тy), и(х,0) — 0, и(х,2)-0. d. u, (0, у) — 0, и(1, у) — 0, и(х,0) —0, и, (х, 2) %35 сos 2 е. и, (0, у) - 0, и, (2л, у) - 0, и(х,-1)-0, и(х,) —1+sin (2xх).arrow_forward15 Find ( T + In y) dydxarrow_forward
- Ex. 3. Find a solution of Laplace's equation, u +u =0, inside the rectangle 0arrow_forward1. Determine the signs (+,- or 0) of r'(t) for the space-curve drawn below: r'(1)=<_ r'(2)=<_ r'(3) =< r'(4)=< r'(5) =< X solve applications. T(1) 1=4 1=5 Z 1=6 Fig. 15 1=2arrow_forward2. U = Uxx OLALA u(dt)=ula, t) = ( ula, 01=0 4t=(2,0) sin a t 70arrow_forward9. The equation of motion of a train is given du by: m=mk(1-e-)- mcv, where v is the dt speed, t is the time and m, k and c are con- stants. Determine the speed, v, given v=0 at t=0.arrow_forward3. Let A be as in (e), Problem 1. Find constants a, b, c such that the curve t (a cos t, b sin t, ce-1/2) is a solution to x' = Ax with x(0) (1, 0, 3). (e) 0 1 -1 0 = -1/2arrow_forward1. The coordinate of a point undergoing rectilinear motion is given by x(t) = t³ – 4t, -2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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