3. Use Laplace Transforms to solve the given differential equations d²x dt² a. b. d²x dt² dx dt +6 +9x = sint, t≥0 subject to the initial conditions x = 0 and = 0 at t = 0 dt - 2 x + 2x = 3e¹ cos 2t, given x(0) = 2 and x'(0) = 5 dt

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A: The solution is given as

Q: Consider the differential equation d²x dx + b. + cx = 0, dt (9.4.5) di2 where b and c are constants.

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A: Solution

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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…

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Q: dy +ky = a sin bx dx %3D Show that the solution of the differential equation is given by: 2 +b²+ab K…

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Q: the fractal differential equation Day + =1/12 and y(0) = 1, Using Laplace transfo

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Q: 1. Let the following differential equation y(4) + 4y" = 0. (*) Verify if the following functions…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: b) Solve the following second order differential equation using Laplace transforms d²x with initial…

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Q: %3D siny(x + siny)dx + 2x²cosydy = 0

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Q: Consider the differential equation dy(t)/dt − ay(t) = B cos ωt + A sin ωt. We would like to find…

A: Given differential equationdydt−ay=Bcos⁡ωt+Asin⁡ωtCorresponding homogeneous equationdydt−ay=0The…

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Q: By taking the Laplace transform of the differential equation initial condition is x (0)=0. If you…

A: I have solved using two methods

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Q: Solve the Cauchy-Euler differential equation d'y dy +2x-20y xr + 2x +1 dx dx

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Q: Suppose U is the subspace of R4 defined by U = Find an orthonormal span ((1, 2, 3,-4), (-5, 4, 3,…

A: Please find attachment

Q: (b) Solve the following partial differential equation. *+ 3 = 5z + tan(y – 3x) ax ay

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Q: Show that the differential equation [y(1+1/x)+cosy]dx+[x+lnx-xsiny]dy=0 is exact.Hence solve it

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Q: (2xy - y² + y)dx + (3x² - 4xy + 3x)dy = 0

A: The given differential equation is