In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
1.
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Chapter 12 Solutions
Bundle: Differential Equations with Boundary-Value Problems, 9th + WebAssign Printed Access Card for Zill's Differential Equations with Boundary-Value Problems, 9th Edition, Single-Term
- 12arrow_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_forward1. Find all singular and all ordinary points of the DE (0.5x²+2x+25)y"+xy'+y=0arrow_forward
- Question 17 Find a parameterization for the line segment from (2, –1) to (1,4). a) Ox (t) = 2 –t and y (t) = -1+5t, tE [0, 1] b) Ox (t) = 2+t and y(t) = -1 – 5 t, t E [0, 1] %3D c) Ox (t) = -2 +t and y (t) =1 – 5 t, t E [0, 1] d) Ox (t) = -1- 5t and y (t) = 2 + t, t E [0, 1] e) Ox (t) = -1 +5t and y(t) =2 – t, t E [0, 1] f) ONone of the above.arrow_forward1. The coordinate of a point undergoing rectilinear motion is given by x(t) = t³ – 4t, -2arrow_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_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_forwardEx. 4. Find a solution of Laplace's equation, u„ +u„=0, inside the rectangle 0arrow_forward2. U = Uxx OLALA u(dt)=ula, t) = ( ula, 01=0 4t=(2,0) sin a t 70arrow_forwardProblem 4. Find y as a function of x if a'y"- 5zy + 9y = x°, y(1) = -9, y (1) = 4. y =arrow_forward20. Calculate the tangent line in point P(2,0) of the conic section x² - 4 x y - y² + 2x - 4y - 8 = 0. Ans. x - 2y-2 z=0arrow_forward3. If z° +x²z+z+y = 0 find (1) əz/əx, (2) əz/əy, (3) ə²z/əx², (4) ə²z/əy?, (5) ³²z/əxəy, and (6) a²z/dydx.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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