%3D xx u15 t) = 14 2. U(XP) =D0 3. Find he fourier senes for -ITLXLO [-TT, T )

Q: Solve the following DE using Laplace Transform: 3. y" — у' — 2у 3D 5 sin x y(0) = 1, y'(0) = -1 -

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Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

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Q: Find the differential of each fuction. a) %3D dy= ? b) U COS U dy= ?

A: Given,  (a) y = s7+8s  (b) y = u cosu  We have to find the differential of each function.

Q: If the substitution u = x/2 is made, the integral 1-(플)2 dx = %3D -

A: Let's integrate.

Q: 2. Use Laplace transform to solve y" + y = 8(t – 27) cos(t) y(0) = 0, y(0) = 1

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Q: Question 3. Compute the integral dz 8+z where y is the rectangle with vertices +3+i with the…

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Q: Q1) Evaluate the integral S S dy dx using polar coordinate

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Q: By using Laplace transform to solve y" + 4y + 8y = sint with y (0) = 1 and y' (0) = 0, what would be…

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Q: By using the Fourier transform, find a solution for the following problem (PJu,(1, x) = ux(!, x) +…

A: The partial differential equation given is as follows: utt, x=uxxt, x+3t2 Apply the Fourier…

Q: F. Change the Cartesian integral to polar coordinate dy dx 171-1 حول من كان الى بولير ار

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Q: Solve by Laplace transform Utt - 9urr = 0, 00 %3D u(0, t) = u(T, t) = 0, u (x,0) = 0, u(x,0) = 2…

A: Use the given information.

Q: y = In(sec t), x = log(cosec t) In(sect), x %3D %3D

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Q: 2. Given that cos pv o v+B? 2B (a) Find the Fourier transform of x+b? (b) Use the result from (a) to…

A: Sol

Q: Use Laplace transform to solve the DE y" + 4y' + 6y = 1 + e¯*, y(0) = 0, y'(0) = 0. %3D

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Q: Compute dy/dx and d^2y/dx^2 for the following parametric functions

A: Given: y=e2tsin2tx=e2tcos2t

Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: -K Owhich methodisused to make U CHA) =\+C 픈 TIX Sin a Solution to the Problem initial and boundary…

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Q: Solve by Laplace transforms. y – 3 | y(T)dr = 4e' sin(2t). %3D 0,

A: by Applying Laplace transformation and inverse Laplace transformation we get the answer

Q: Solve the following IVP (without Laplace Transform): d'y , dy - 2y = 6 cos 2t + 2 sin 2t, y (0) =…

A: Solution: Given ivp is

Q: Use the Laplace transform methods to solve the equation: y +y = 2 sint, y (0) = 1 O y = 2et + sin t…

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Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

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Q: 2. Convert the integral In(r² + y? + 1) dx dy into a polar integral and then evaluate it

A: Explained below

Q: general solution (without Laplace Transform): dy dy +2+ 5y = 2e-t. dt dt2

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Q: -2-x Q1) Evaluate the integral S* dy dx using polar coordinate 0,

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Q: y" - 2 y' + 2y = 4 cos 2t + 2 sin 2t , y (0) = 1 , y' (0) = 1 %3D

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Q: y = logt, x = t -4 %3D

A: Let the given function be, y=logtx=t-4 Put x+4 for t in the function implies, y=log(x+4)

Q: d/dt [sec^3(t)] compute the derivate

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Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

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Q: Solve the following DE using Laplace Transform Method. Show your complete solution y" -2 y' +2y = 4…

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Q: 13( 3sin x 1 de 4 % sin 3x dx 4

A: According to the given information it is required to find the integration:

Q: Use the Laplace transform to solve y" + 9y = cos 3t, y(0) = 4, y'(0) = 2. %3D %3D %3D

A: Given that, y"+9y=cos3t, y0=4,y'0=2

Q: 2. Use Laplace transform to solve y" + y = 6(t – 27) cos(t) y(0) = 0, y'(0) = 1 %3D %3D

A: We have to find the solution of the given initial value problem. y"+y = δ(t−2π)cost With initial…

Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

A: In this question, we have given a computer-generated direction field for the differential equation…

Q: The equation y" + 4y'+ 6y = 2et where y(0) = 5,y'(0) = 0 when solved using Laplace transform,…

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Q: eiz dz around (a) |z – in| = 2 (b)|z - | = 2 (c)|z| = 2 sinhz

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Q: If u=lx+my and v=mx-ly,show that 1? + m? ди ди 1 + m?

A: Given  u = lx + my v = mx - ly

Q: 2. cos(2t) + 7 sin(3t)

A: we have used laplace property and table for this question.

Q: Solve for the Laplace transform of e2t sin t cost cos 2t cos 4t

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Q: Solve by using the method of Laplace transforms: y"+9y = 2x + 4; y(0) = 0; y'(0) = 1 %3D

A: We need to solve the given IVP using Laplace transform. Some of the know Laplace transformation…

Q: I = 1- 6x?y dx dy.

A: In double integration, we start integrating from the inner part with respect to the inner variable.…

Q: Give the solution of ODE by using Laplace transform method; y' + 2y = 2 e2t ,y(0) = 0 %3D

A: Properties of the Laplace transform  Lf'(t)=sF(s)-F(0) L-1n!(s-a)n+1=tneat Leat=1s-a

Q: Q6 de +y = Cos(t), y(0) = 0, y'(0) = -1, Use Laplace Transform.

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Q: a) Sojlve the initial vajlue problem using Laplace transform UTM y + 2y = 26 sin 3t, y(0) = 3. UTM…

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Q: Con Sider the in itial volue problem: X = 2x, +3xz+5e? X,(O)=1 X =3x,+2xz=6e“ x,(6)=-2 131 %3D find…

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Q: Q1) Evaluate the integral S dy dx using polar coordinate

A: We have convert the given problem into polar coordinates.

Q: Solve the equation dy y %3D dx xy-3 II +

A: Using given transformation

Q: By using Laplace transform to solve y + y = cosht y (0) = 0, what would the particular solution be?…

A: the given equation is y'+y=cosh t  y(0)=0 taking Laplace of the given transform Ly'+y=Lcosh t…

Q: Calculate the Laplace transform of_ƒ(t) = t². (Note, you will have to integrate by parts twice.)

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Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0