Q13. If u= u(x,y) then the partial differential equation 2u, u, is of the kinda) Hyperbolicb) Ellipticc) Parabolicd) cyclicQ14. The solution of the differential equation y (1-x)+yx-y=0 is given bya) y = ze*b) y = 46²xc) y = 2x³d) y = 2x³-2-

Given partial differential equation .We have to determine the kind of partial differential…

Answered: Q13. Ifu= u(x, y) then the partial…

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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8. Find the solution of the differential equation (D* - 2D° + D*)y = 0 y = C, + C2x + e*(C, + y = C+ Cx + e*(C, + C. %3D A. Cex) B. Y = C, + Cx + e*(C, + C4x?) y = C + C,x² + e*(C; + В. C4x) D. C4x)
A Function 4(*) Satiskies the differential equation dy d+ = - 4y - 3y ³ + 128 y ² 3 a) what are the constant Solutions? b) For what values is y increasing? -
(15,00 Puanlar) 3- Solve the differential equation (D - 9)y = 3e -3z 3z a)y= Cie + cge - re 3z b)y Ce + ge 3z +ce 3z 3% c)y= Cie -3z d)y = cie + cze +e 3z a) a) b) b) C) c) d) O d) eBoş bırak KÖnceki 3/6 Sonraki> Kapat VSinavı Bitir
6. Is the differential equation exact Cos y dx + (y? - x sin y) dy = 0 a) no b) for y=x siny c) yes d) at x-D0 7. solution for the differential equation ( 2xy- sin x ) dx + (x2- cos y) dy = 0 a) x'y + cos x – sin y = C c) xy2 - cos x - sin y = C. b) xy? + cos x- sin y = C d) x²y + sin x - cos y = C 8. consider the differential equation x*y3 + x(1+ y?) = 0 Which of the following integration factor makes the equation exact %3D dx a) b) 0) d) xy:
please do b) only
The following excupt One are exact differential equations · Which one ts not? 4) (I+y?+xy?) dx +(x?y +y+2xy) dy も)(4メリ+メ8)x+(xナ)dy =D c) (xy?+y-x)dx + x (Xy+1 )dy=o D)(7ースメリーリ2)y- (x+y)ayこ0
n2
Consider the following second-order partial differential equation : 1 yu - 2aryu.y + auyy ry (yu, + r*u,), > 0, y > 0. (G) 1. The equation (F) is : a) Hyperbolic Equation b) Parabolic Equation c) Elliptic Equation d) None of the above 2. The characteristics equations corresponding to (G) are: a) # = and = -2. b) = 3 and d = 4. %3D c) = d) None of the above. 3. Using the change of variable a = r² + y? and B = y, the canonical form of (G) is: a) u33 +ua = 0. b) uga +ua = 0. c) ugs -Jug = 0. d) None of the above. 4. Let f and g two arbitrary real valued functions. A general solution of (G) is: a) u(r, y) = f(r2 + y²) + y²g(x² + y?). b)u(r, y) = f(x) +ag(22 + y?). c) u(r, y) = f(y) +?g(a² + y?). d) None of the above.
7. Find the functions M(r, y) and (x, y) such that each differential equation is exact: (a) M(r, y)dr + rey + 2ry + dy = 0 1 (b) |dr + N(x, y)dy = 0 2 +y
5. Determine the differential equation of minimum possible order linear homogeneous differential equation with real coefficients if two particular solutions are e"cosr and e-sinx.

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Q13. Ifu= u(x, y) then the partial differential equation 2uu, is of the kind a) Hyperbolic b) Elliptic c) Parabolic d) cyclic