In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.
3.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- Ex. 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_forward9. 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_forward2) 3 3 dr+du+ +y=t dr subject to x = 1 and y = 0 at t = 0arrow_forward
- 15 Find ( T + In y) dydxarrow_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_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_forward
- Solve Laplace's equation, = 0,0arrow_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_forward1. The coordinate of a point undergoing rectilinear motion is given by x(t) = t³ – 4t, -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_forwardProblem 9. Find a parametrization of the curve of intersection of x = √y and z = √y from (1, 1, 1) to (4, 16, 2).arrow_forward2. A bug is crawling along the surface defined by x³ + y²z – z³ = 5. The bug is currently at the point (2, –2, –1). (a) If the bug moves along the surface by increasing its y-coordinate and keeping x = quickly is its z-coordinate changing? = 2, then how (b) If, instead, the bug moved from (2, –2, –1) along the surface by increasing its z-coordinate, and keeping y = -2, then how quickly is its x-coordinate changing?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSONThinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education