Solve the wave equation, 18²u 4 Ət² with the initial conditions Check 8² u მ2 u(x, 0) = cos(x), Vx du(x, 0) Ət using the d'Alembert solution. u(x, t) = = x exp(-x²), V.

Q: du dx PDES du (0, t)=0=(2n, t) dx i.c.: u(x, o) = f(x) du i. c. : (x,0) = 0 dt Please write solution…

A: Wave PDE is ∂2u∂t2=∂2u∂x2 with conditions ∂u∂x(0,t)=0=∂u∂x(2π,t) i.c. : u(x,0)=f(x)i.c.: dudt(x,0)=0…

Q: b) (12xy2+64+se*)do + CGx?y+2x)dy=0 c) 24 dx + (6x³¬xy•xdy=0

A:

Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" +…

A:

Q: Calculate 2 4-y2 dyde Jsydxdy. O 1-X T Sinx x.Sin.dy.dx y dydx..

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

A:

Q: (77) (04-70° + 180² - 200+ 200+8) V = 0

A:

Q: Solve the following boundary based problem: = k (wrr +=w₂ + 1/2 wee) Wt Subject to the following…

A: Given The differential equation is wt=kwrr+1rwr+1r2wθθ ⇒∂w∂t=k∂2w∂r2+1r∂w∂r+1r2∂2θ∂θ2 subject to the…

Q: 4t-5 b) Find for y = sinvt – 1, and x = dx cost b) Find dx for sin?x – cos?y = tanx Jz dt %3D t+2

A: We have to find dydx (1) y=sint-1 and x=4t-5cost (2) sin2x-cos2y=∫ytanx31t+2dt

Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

A:

Q: PART 1: State the characteristics (order, degree, type) of the given DE. 1. (1-x)y" - 4xy' + 5y =…

A:

Q: (у — siny)(y'сosx — cscy) :

A: Solve the differential equation                          (y'-siny)(y'cosx-cscy)=0

Q: Fix c > 0. Show that for any constants a, ß, the function u(1, x) = sin(æct + B) sin(æx) satisfies…

A: We have the function u(t,x)=sin(αct+β)sin(αx) . We have to show that this function satisfies the…

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

A:

Q: Under suitable assumptions derive one dimensional wave equation.

A:

Q: Use approbriate ferm of chain rule to fird %3D

A: Given  z=cos(x)sin(y)x=u−vy=u2+v2

Q: dw 4w A) Give the general solution of dx = x³. B) Solve y' + = y²x³.

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: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: udv – v(1 + v cos 2u)du = 0

A: We will find out the required solution.

Q: Solve Non-Exact DE: udv – v(1 + v cos 2u)du = 0

A: Solve Non-Exact DE: udv – v(1 + v cos 2u)du = 0

Q: A) find dy 2x2y+ sin y=2x² U=2x-2 to find dx dy B) use the chain rule y = 2u2-3u+ 4 dy dx C) Find…

A:

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

A: Variable separable differential equation

Q: 1. y = 5u°; u=7x – 4x' + 2x –9 2х-9 u +1. u=Vx? +1 y = u? -1' 3. x=7y -3y +y +8 2.

A:

Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

A:

Q: A suspension bridge swinging in the thunderstorm can be modelled by the following equation:…

A:

Q: Solve the inhomogeneous wave equation on the real line Utt − c 2Uxx = sin x, x ∈ R U(x, 0) = 0,…

A:

Q: Əz and Əx az #4. Calculate given that ду x² sin (z) + (x² – 1) y* = 2°.

A: