Q.4 Solve the wave equation: X U₂ = Uxx +1+t−=(1+e'), U (0,1)= I X U(x,0) = — , U₁(x,0) = T X 0-52. U (л,t) = e' T

Q: (1-x)y' = y²

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: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

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Q: Solve the wave equation a². u(x, 0) = u(0, t) = 0, u(L, t) = 0 10hx L | 10h (1 − ²), 1/2/³ - x ₁…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: What is the integrating factor of the equation (2xy*ev + 2xy³ + y)dx + (x²y+ev – x²y² – 3x)dy = 0 A…

A: We have to choose the correct answer from the given option according to the given condition

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

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

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Q: b) Determine the characteristic equation for y" + 3y + 2y = 0. c) Find the general solution for y" +…

A: The differential equation is:To Do:Determine the characteristic equation and solution to the given…

Q: Which is the linear differantial equation into which the Bernolli differantial equation transforms

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Q: (у) ну- (-см ) - уве Сай

A: Given differential equation is xy - dydx = y3e-x2

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A: (a) Solve the differential equation as follows: Let p=dxdt, or, x'. Differentiate it with respect to…

Q: 4) = sec(x + y) dy dx 2x-2y+1 5) y' %3D x-y

A: See the detailed solution below.  For others, re-upload the question.

Q: poin If g(u) —D V9u + 3 then g' (u) =

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Q: Consider the wave equation 00, with (0,r) =(71) = 0, m(x,0) = sin x and -0 at -0. Then is

A: Given wave equation, ∂2u∂t2=3∂2u∂x2 , 0<x<π, t>0withu0,t=uπ,t=0andux,0=sin x, ∂u∂t=0 at t=0…

Q: x' Construct the phase plane for the points (2,2), (2,0), (2,-2), (0,2), (0,-2), (-2,2), (-2,0) and…

A: According to questionWe have to draw the phase plane for the given points.

Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

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Q: 3.8. Question. Match equations y' = sin x, y' = cos y, y' = y cos(x)· a) c) b) to direction fields.…

A: To find the direction field of a differential equation you first need to isolate y' from the…

Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

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Q: A suitable substitution to transform the L 0² r' = r? + 2r 0² into linear equation will be: 0-2 rー1…

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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: 1.) d³s dt3 2.) x 3.) ди ду d²v dr² + U = EQUATION S 3 1 + (- 2² z əx² dv + t dr 13 ds dt 4 - st = 0…

A: Since you are asking multiple questions. We are answering only first three questions as per our…

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)…

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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

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

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Q: Solve for the higher order DE number 2

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Q: Find dx * and then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t? –…

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Q: Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,…

A: Given partial differential equation or wave equation is 13∂2u∂x2 -8 ∂2u∂t2=0 -----(1) Also, given…

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

A: Solving the problem by finding the derivative.

Q: Determine the general solution: (dx/dt)A3 - (dx/dt)^2 - 4x = 0 Select the correct response: O y= c1…

A: Topic:- differential equations

Q: NAME: dy IN QUESTIONS 1-13, FIND dx 1 2. у 3D х6-6х+4

A: Derivative problem.....

Q: Solve the inhomogeneous wave equation on the real line Utt − c2Uxx = sin x, x ∈ R U(x, 0) = 0, Ut(x,…

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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: The equations re + uz – cos(v) – 2 = 0 and u cos(y) + 4r?v – 5yz2 – 1 = 0 can be solved for (u,v) as…

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Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00

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: Solve  using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)

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Q: у" + 4y' + Зу %3D sin (e*)

A: