In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
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Chapter 12 Solutions
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_forwardPROBLEM (1): If =2 z-x'y and Ā = 2 xî-3 yzj+x z°k, find A.V and A xV4 at the point ( 1,-1,1). PROBLEM (2):arrow_forward4. Find the velocity and acceleration of a particle whose position function is x(t)=sin(2t)+ cos(t)arrow_forward
- 3. Find two Frobenius solutions for a²y" + (x² + æ)y/ – y = 0, x > 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_forward7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b) (d) x² + y² = 4(x - y) (x - 2)² + (y-2)² = 4arrow_forward
- 15 Find ( T + In y) dydxarrow_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_forward
- 1. The coordinate of a point undergoing rectilinear motion is given by x(t) = t³ – 4t, -2arrow_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_forwardSolve Laplace's equation, = 0,0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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