3 Find the bounded Solution of o учу j²y аха = xt dt² sy( dy where y(x, 0) = and y (o₂t) = 0 (x,0) St x>0,t>o = 0

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

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Q: Determine whether the process ~ X(t) = cos(wt); where w wide-sense stationary or not U(0, 1), is

A: According to the question,

Q: 46. ty" + (t-1)Y'Y = 0, Y(0)5, Y() = 0. Ans. Y 5e-t

A: As per our guideline we can solve only first question for you. Please repost for another question.…

Q: 4v2 - 1 d)u =x²y" + xy + (x² – v²)y u" + (1.

A: Given that  LHS=u''+1-4v2-14x2u Simplify that to get,…

Q: 6) Find f(x) for f(x) = sec(vx2 + 1).

A: We are solving the first question and for the next question post the question again and alsomention…

Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

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Q: ƏF Find at (x, y) = (T, 1) if f (x,y) = cos vt dt. cos yt dt. ww

A: given,          fx,y=∫0x2ycostdt

Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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Q: If F (x)= [V5t² – 3t dt find F'(3). a) 0 b) Viz c) d) 3 e)

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Q: Calculate the frist order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3

A: First order Partial derivatives

Q: xydx - (x^2+3y^2)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)dx + N(x,y)dy…

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Q: Use the solution of the vibrating string with fixed ends obtained with separation of variables to…

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Q: If L(x, y, y/) = y² (1+ (y/)²)³ what are Ly and Ly? O Ly = 2y(1+ (y)²)³ and Ly = 6y"y² (1+ (y')²)² O…

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Q: ",=a'u, O0 (19) (0.1) = 0, (L)= u(z,0) = S()

A: Note: According to our guideline policies we can answer only first question. (19) This question is…

Q: 4- Find du if Z z = e w: Z = sin(xy) x=t J = Int 5- Find a, b and C if w. a.tan (x²+¹1)_boxy + Cayin…

A: Note: - According to the company policy we can attempt only one question so please upload the next…

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

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Q: Solve au_a²u əx² Ət __U(x,0) = = " 0 0, subject to the conditions U(0,t) = U(6,t) = 0, Interpret…

A: Using crank Nicolson method to calculate the numerical solution for ∂U∂t=∂2U∂x2  , 0<x<6,…

Q: Which of the additional conditions below can be used to obtain a clamped cubic spline S(x) passing…

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Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: Assume that u = U (x,y) iu differentiible and x =r ca Ô and y=rsin o eapress 2. entinely in termv 0…

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Q: dy / dx

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Q: b) f(x, y) = e²=²+v, u= (1,0). %3D

A: We have to find the directional derivative

Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

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Q: dr/dt=3/2(t+3)^1/2 i+e^t j, initial condition:r(0)=0

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Q: Show that f(z) = x³+i(1−y)³ is differentiable only at x = 0, y = 1 and f'(z) = 0.

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Q: Which of the following is the integrating factor A(x) to be used for the general solution of the 1…

A: Consider the provided question, y'+15xlnxy=e-x5xdydx+15xlnxy=e-x5x On comparing with dydx+Pxy=Qxwe…

Q: What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

A: Ft,y=-y22tDomain:{t,y∈R2:t≠0}∂F∂y=-ytDomain:{t,y∈R2:t≠0}∴function Ft,y is continous.So there exists…