The general solution of the wave equation of the form titt = Uxx, - co

Q: 5) y"-y'-2y=x+cosx

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Q: アrova solution to if ulx,t)= (sin (x- 6 )-Sin (x+6)) tion equa %3D

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Q: • The Doman of f(x) = 4-Vx is 1. (2, co) 2. [-2, c0) 3. [2, 0) 4. [-2,2]

A: The domain is the set of all values of x for which the value of function f(x) exists.   For f(x)=4-x…

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 5. Let z1 = a1 + b;i and z2 = az + bzi. (a) Find Im[z,Zz + (Z)? – 2,7 ]. (b) Prove that (z)² = z,² .

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: (Do solution short form)Prove that the only idempotent elements in an integral domain R with unity…

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Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

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Q: The two-dimensional wave equation string is describing the vibrations of an infinite 2²n 20² n Ət²…

A: Since you have asked multiple questions, we will solve the questions (i) and (ii) for you. If you…

Q: Find the solution. (D³ - D']y = 0 y = c, +cx+czx²+c,e'+cge" y = (e, +c,)xe* +czx +c,e +cge* (c y =…

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Q: y" + 4y' + 3y = sin (e*) %3D

A: follow next step

Q: Problem : If f(r, y, z) = In( + y° + z^) + v(® +y! + z®), then find fz, fy and f, at (1, 1, 1).

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Q: (2) Sketch the direction field associated to the system I'=x²-y-3, y = y + x² - 5. Include the…

A: sketch the direction field associated to the system    x' = x 2 - y - 3 y' = y + x 2 - 5   include…

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cost U (x, 0) = 0.

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Q: (Section 17.3, 17.5) Consider F(a, y) = (e-" cos(y))i + (e-" sin(y))} (a) Show that F is…

A: Here is the solution of the given problem. Line integral:  Conservative Vector Field:

Q: QUESTION 4 a) Let (27¹) Calculate the products A. B and B. A, and the determinant det (A). b)…

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Q: (a) V (fh)= fVh+2Vf.Vh+hV²f,where f and h are scaler fields.

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: Q5) Solve the wave equation for vibration of organ pipe subject to the boundary condition:

A: In this question, we solve the wave equation by using the method of separation of variables.

Q: x2 + 8x +3 10) y=- _ dy A) 3x2 + 8x - 3 dx X Find the derivative. A) 11) s= t3 tan t-√√t ds dt C) dy…

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Q: Find the equations of the reflection in the line y=x+1. a) x' = y - 1 , y' = x + 1 b) x' = x - 1 ,…

A: Given: Equations of the reflection in the line : y = x + 1

Q: 7. Find the general solution of (Dʻ + 2D’ + 10D²)y = 0.

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Q: In what form should the particular solu tion be sought for the equation y(1) + 2y" + y" + 2y' =…

A: Consider the equation y4+2y'''+y''+2y'=xe-2xThe characteristics equation of the homogenous equation…

Q: The system x' = cos(t)x+ sin(t)y y' = cos(t)x - sin(t)y is linear.

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Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

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Q: (2) Consider the following vector ODE 2 1 1 Y': × - (D) - - () 0 2 -1 Y + 0 0 0 -1 (a) Convert it…

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Q: If I(x) = | u"-1e-" du, therefore 0, r°(x) = (u*)*-e" du du -u? 0, O Option 1 r°(=) = (u")** e " du…

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Q: d[cos(x*)] dx (2k+1)! (-1)*2,* - (2k)! .(-1)시2x4~2 (2k+1)! (-1)*2x*-3 E (2k+1)! None (-1)*-'2x*-1 E…

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Q: If y = (cos (2³) + 3)4, then equals dy dt a) 4 (cos (2³) + 3) ³ (x²) b) 4 (cos(x³) + 3)³ (-sin(x³))…

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Q: 11. Evaluate * d²y dy - 2 + 5y = –17sin2x dx2 dx y = (C,e* + 68 |cos2x +(Cze* + 17 sin2x 15 y =…

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Q: In what form should the particular solu tion be sought for the equation y(4) + 2y"' + y'" + 2y' =…

A: We will solve it by undetermined coefficient method Let the particular integral with respect to x is…

Q: a) O Show that the wave equation Ytt = a²Yzz where a is a constant, can be reduced to the form Yuv =…

A: Use chain rule in a  and integration in b .c can be solved by substitution of t=0.

Q: Find the solution of the wave equation when initial velocity equal to O and initial deflection is…

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Q: (0,1) 12. (3x – y+ 1) dx – (x + 4y + 2) dy J(-1,2)

A: Since you have asked multiple questions in a single request so we will be answering only first…