please send complete step by step handwritten solution for Q1 1. Solve the initial-boundary value problemди2 3u0 03 dx2u(0, t) = u (4, t) = 0t>0(7)3Txu(x, 0) = 5 sin15 sin40 < x < 42. Solve the initial-boundary value problem= 400-Əx20 < x < 67, t > 0и(0, t) — и (вт, t) — 0t>0диx, 0) = 600 sin()2x+ 800 sin3u(x, 0) = -50 sin(x),0 < x < 6T

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Answered: 1. Solve the initial-boundary value…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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13. The standard form of 3dy-xydx = 3y3e4x/3 by Bernoulli's equation is:
Match column B with the correct answer on column A, write only the capital letter of the answer on the blank provided at the left side/right side of the test paper. Match from column A the solution of the differential equations on column B. Column A A. xlnx + ylny = c B. 2y = x4 + cx2 C. e(x^2) + y2 = c D. x2 = cy3 E. x2 y = 2x4 + c F. ylnx + xlny = c G. x2 (x2 + 2y2) = c H. x (y + x2) = c (y – 2x) I. xy2 – x2y + 3x2 – 2y = c J. xy3 = 2y2 + 4y + 4 + cey K. y (x2 + c) + 2 = 0 L. (y – x) (y + 3x)3 = cx3 M. x2 y = 2x2 + c N. x (y + 1) = (1 + cx) ey O. e(-x^2) + y-2 = c P. (y + x2) = c (y – 2x) Q. x2y2 + 2xy – x2 = c R. x4 = c2 (4x2 + y2) S. x2 (x+ 2y) = c T. x2 + y2 – 3xy = c Column B (x – y) (4x + y) dx + x (5x – y) dx = 0 xy3 dx + e(x^2) dy = 0 y dx + (3x – xy + 2) dy = 0 2 (2x2 + y2) dx – xy dy = 0 (x2 + y2) – xy dy = 0 (2x – 3y) dx + (2x – 3x) dy = 0 x2 yy’ = ey (x4 + 2y) dx – x dy = 0 (3x2 – 2xy + 3y2) dx = 4xydy
Match column B with the correct answer on column A, write only the capital letter of the answer on the blank provided at the left side/right side of the test paper. Match from column A the solution of the differential equations on column B. Column A A. xlnx + ylny = c B. 2y = x4 + cx2 C. e(x^2) + y2 = c D. x2 = cy3 E. x2 y = 2x4 + c F. ylnx + xlny = c G. x2 (x2 + 2y2) = c H. x (y + x2) = c (y – 2x) I. xy2 – x2y + 3x2 – 2y = c J. xy3 = 2y2 + 4y + 4 + cey K. y (x2 + c) + 2 = 0 L. (y – x) (y + 3x)3 = cx3 M. x2 y = 2x2 + c N. x (y + 1) = (1 + cx) ey O. e(-x^2) + y-2 = c P. (y + x2) = c (y – 2x) Q. x2y2 + 2xy – x2 = c R. x4 = c2 (4x2 + y2) S. x2 (x+ 2y) = c T. x2 + y2 – 3xy = c Column B (x – y) (4x + y) dx + x (5x – y) dx = 0 xy3 dx + e(x^2) dy = 0 y dx + (3x – xy + 2) dy = 0 2 (2x2 + y2) dx – xy dy = 0 (x2 + y2) – xy dy = 0 (2x – 3y) dx + (2x – 3x) dy = 0 x2 yy’ = ey (x4 + 2y) dx – x dy = 0 (3x2 – 2xy + 3y2) dx = 4xydy (1 + lnx) dx + (1 + lny) dy = 0
Match column B with the correct answer on column A, write only the capital letter of the answer on the blank provided at the left side/right side of the test paper. Match from column A the solution of the differential equations on column B. Column A A. xlnx + ylny = c B. 2y = x4 + cx2 C. e(x^2) + y2 = c D. x2 = cy3 E. x2 y = 2x4 + c F. ylnx + xlny = c G. x2 (x2 + 2y2) = c H. x (y + x2) = c (y – 2x) I. xy2 – x2y + 3x2 – 2y = c J. xy3 = 2y2 + 4y + 4 + cey K. y (x2 + c) + 2 = 0 L. (y – x) (y + 3x)3 = cx3 M. x2 y = 2x2 + c N. x (y + 1) = (1 + cx) ey O. e(-x^2) + y-2 = c P. (y + x2) = c (y – 2x) Q. x2y2 + 2xy – x2 = c R. x4 = c2 (4x2 + y2) S. x2 (x+ 2y) = c T. x2 + y2 – 3xy = c Column B 2y dx = 3x dy (y2 – 2xy + 6x) dx – (x2 – 2xy + 2) dy = 0 2(y – 4x2) dx + xdy = 0 y' = xy2 (xy2 + y – x) dx + x (xy + 1) dy = 0 (x – y) (4x + y) dx + x (5x – y) dx = 0 xy3 dx + e(x^2) dy = 0 y dx + (3x – xy + 2) dy = 0 2 (2x2 + y2) dx – xy dy = 0 (x2 + y2) – xy dy = 0 (2x – 3y) dx + (2x – 3x) dy = 0 x2 yy’ =…
Module 4 Obtain the solution of the following differential equations. 4. (3x + y − 2)dx − (3x + y + 4)dy = 0
Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete and Step by step solution please)
obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the particular solutions . y=2e^x cos3x
In Problem, we have provided the slope field of the indicated differential equation, together with one or more solution curves. Sketch likely solution curves through the additional points marked in each slope field.
Suppose m1 =4 , m2 = -5, m3= -2 are roots of multiplicity one, two and three of an auxiliary equation. Write down the general solution of the corespoinding homogeneous linear differential equation with constant coefficents.
Attached below is a description and the necessary differential equations systems problem. What is the general solution of the 2x2 system: X' = [ Row 1: -1 10, Row 2: 1 2] * X ? What is the solution that satisfies the intial conditions (x(0),y(0)) = (0,-7) ?
Find a homogeneous linear differential equation with constant coefficients whose general solution is given: y = C1cosh 7x + C2sinh7x y = C1 + C2e2xcos 5x + C3e2xsin 5x y = C1cos x + C2sin x + C3cos 2x + C4sin 2x
4). Write the first-order differential equation in standard form. (Use yp for y'.) y' = x9y + sin(x) please show show step by step .

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1. Solve the initial-boundary value problem du 2 32u 0 0 3 dx2 u(0, t) = u (4, t) = 0 t > 0 u(г,0) = 5 sin 15 sin 0 < x < 4 4