34. Solve the following problem: - Utt = uxx Ut+ux, 00, u(0,t) = 0, u(3π/2,t) = 0, u(x, 0) = cos x, ut(x, 0) = x² - (3π/2)². Explain its physical meaning.

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

Q: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

A:

Q: Find one solution of y" + 2y' - 2y = 3e³* cos(2x).

A:

Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

A:

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

Q: Find the solution Py = ²84, u a 81² ul₁=0 = sin ³7.x, ди du |-o = x(1 − x) (0 < x < l), u(0, t) =…

A:

Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

A:

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

A:

Q: I need the answer as soon as possible

A: As we know that, eiz=cosz+isinz                   ...(1)And,e-iz=cosz-isinz                ....(2)…

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

A:

Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

A:

Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

A:

Q: Q.1) The general solution of the equation e' cos , is:

A:

Q: Solve

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Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

A:

Q: Q2) Find the general solution for this equatio- y" + (tanx-2cotx)y' + (2cot²x)y = 0 If you know that…

A: Given differential equation It has one solution Lets use method of reduction of order.Assume the…

Q: (2 sin(y)) dx + (x y cos(y²)) d y = 0

A: Variable separable differential equation

Q: 4. a) Find the general solutions of the following differential equations. Express the general…

A:

Q: q2-  91.2% of 1980 is: Select one: 18057.6 180576 180.576 1805.76 18.0576

A: We are asking to find 91.2% 0f 1980

Q: Find the solution. dy 2y + dx -=x²y²sinx 1 (A) y = х? (sinx - c) B y = x ( sinx +c) y = x²(cosx+c)…

A: We have to find solution of given D. E.

Q: (b) 9-(t+1) (42t - sin t)dt

A: Given that the integral is .The objective is to evaluate the given integral.

Q: Show that y sin x is a solution to xy" + (2 secx)y' + xy = 2. =

A:

Q: A particular solution of y" - 3y' – 4y = 2sinx 5 -cosx 17 a. 3 COSX - 17 5 sinx 17 b. 3 -sinx 17 C.…

A: find roots for the homogeneous system

Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

A:

Q: Let u(g) and v(g) be the Fourier transforms of u(x) and (2) of the product u(z) v(x)? Select one: O…

A: