Q.4 Solve the wave equation: Uµ =U« +1+t− ² (1 + e'), π U (x,0) = ---- U (0,t) = 15/2/₁ U(n,t)=e¹ U₁(x,0) = T T

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…

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A: (a) To solve the given differential equation: Let   p=dxdt, or, x' ⇒dpdt=d2xdt2 ... differentiating…

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A: Given Differential equation (1-x)y'=y² This can be written: (1-x)dy=y^2dx; separating the variables:…

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A: We will find out the required solution.

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A: NOTE: Horizontal axis is t-axis  .

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A: Given

Q: (5) (--) A particle is traveling with acceleration d(t) particle was at the origin, (0) =(0,0,0),…

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Q: (b)Find orthogonal trajectory of x'y = c.

A: The given problem is to find the orthogonal trajectories of x2y=c.

Q: 6) —— (y² + z²)u₂ +xzu₂ − xyu¸ = 0

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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: e an is a solution or dirrerential equation y'ray=20* how?

A:

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

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Q: (у — siny)(y'сosx — cscy) :

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

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

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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)…

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Q: The second order homogeneous Cauchy-Euler equation defined by: 2d²y +bx- dy ォマ +cy=0 dx2 dx (ay"…

A: We have to choose the correct answer

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Q: Solve

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Q: Solve for the higher order DE number 2

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Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: c2 dt² dx² ||

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Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: Consider the Riccatti equation  v'= v^2-7v/x +8/x^2 a) Use the substitution  v= y'/y  obtain the…

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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.

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Q: 3x'y*dx + (2a°y + 4y*)dy = 0 Oa²y³ + y* = c Oa'y? + y* = c Oa'y? – y* = c Oa²y³ – y* = c 2.3

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Q: ignments: Find a solution for the following equations in two different ways: analytically and…

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

Q: - (D' - 4)y = x'e"

A:

Q: Consider the differential equation y' = 2y X a) Sketch the slope-field for x in [−2, 2] and y in [0,…

A: Given: Differential equation y'=2yx. To do : a) Sketch the slope-field for x in [-2, 2 ] and y in…