Find dw/dt at t 1 if w xe + ysinz - cosz, r ! = 2/t, y = t – 1 and z = nt.

Q: dx 1s+ kıl35-x) +kaly-x) dy %3D dt k, , k. k3 are Con Stants.

A: Given system is dxdt=15+k135-x+k2y-xdydt=k2x-y+k335-y Here, 1k1=5⇒k1=151k2=10⇒k2=1101k3=5⇒k3=15 So,…

Q: Use the Laplace transform to solve the initial value problem. (a) y" – y' – 6y = 2, y(0) = 1, y'(0)…

A: Laplace transform

Q: dy S2) +y cos(t), y(0) = 1 solve the initial value problem using the Laplace and inverse dt Laplace…

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Q: (a) Solve for the initial value problem by using Laplace transforms method у"- у'- бу %3DSin 2t y(0)…

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Q: use the laplace transform to solve the initial value problem y"+2y'+2y=cos(2t) with y(0)=0 and…

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Q: A bee with velocity vector r'(t) starts out at (−4, 0, 5) at t = 0 and flies around for 5 seconds.…

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Q: Find the IVP for the differential eqution X' y' - 3xy'+68y=0, that satisfies the initial conelition…

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Q: Use the Laplace transform to solve the initial-value problem, у" — Зу' + 2у — sin(t); y(0) %3 0, у'…

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Q: 6. Use Laplace transforms to solve the initial value problem, 4t, 0<t<1 y' +2y = f(t), y(0) = 0,…

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Q: dw 3) Find dt if w 5 cos(xy) – sin(xy), x =,y = t, z = t3 at at 4) Let t =,u = x² - y? ,v = 4xy³.…

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Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: Consider the ode: dy In(t – 1) dt y + 1 For what initial conditions are we guaranteed that a unique…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 2y" – y' - 2y = sin(4t),…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 4y = sin tu(t - 2π), y(0) =…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin(/2t), y(0) = 11,…

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Q: Find the general solution of dt z(t) = Az where z = y(t and A =

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Q: The solution of the differential equation using Laplace transform dy 10y = 12e is %3D given that…

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Q: If s(0) dt: 20z 4, then f (t) dt is -3 E) divergent

A: A)  6

Q: Use the Laplace transform to solve the initial value problem. y" – y' – 6y = 2, y(0) = 1, y'(0) = 0…

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2 y(t) %3D

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Q: Use the Laplace transform to solve the initial value problem y" – 2y' – 8y sin 3t, y(0) = 0, y'(0) =…

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Q: Use the Laplace transform to solve the initial value problem y" + y' – 2y = e# with y(0) =1 and…

A: Given differential equation :

Q: Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin(2t), y(0) = 11,…

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

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Q: Use the Laplace transform to solve the initial value problem y" + 4y = e2t, y (0) = 1, y' (0) = -1.

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Q: The solution of the differential equation using dy + 6y = 7e-3t is dt Laplace transform „given that…

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Q: Use the Laplace transform to solve the given initial-value problem. y" +y = 2 sin(2t), y(0) = 11,…

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Q: Find dw/ dt at t = 1 if w = xey + y sin z - cos z, x = 2sqrt(t), y = t - 1 + ln t, and z = pt.

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Q: Use the Laplace transform to solve the given initial-value problem. y"" + 2y" – y' - 2y = sin(3t),…

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Q: Use the Laplace transform to solve the given initial-value problem y" + y = 2 sin(2t), y(0) = 11,…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 4y = sin t U(t – 2n), y(0)…

A: We will find out the required solution.

Q: use the Laplace transform to solve the initial-value problem y" + y = 6 + y(0) = 0,y'(0) = 0

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Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, ln (t + 1).

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Q: d?y = v2sin/2t; with y(0) = 10, y(1)(0) = 0 %3D dt2

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Q: Use the Laplace transform to solve the initial value problem below. y" – 2y' + ly = t, y(0) = 0 ,…

A: Given : differential equation              y''-2y'+y=t               --------- (1) with…

Q: Use the Laplace transform to solve the given initial-value problem. y"+y= √2 sin(√2t), y(0) 13,…

A: Solution:-

Q: Use the Laplace transform to solve the given initial-value problem. y""+ 2y" - y'- 2y = sin(4t),…

A: To use: Laplace transform to solve the given initial-value problem. y'''+2y''-y'-2y=sin4t, y0=0,…

Q: Use the Laplace transform to solve the given initial-value problem. dy - y = 1, y(0) = 0 dt y(t) =

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Q: The solution of the differential equation using Laplace transform + 6y = 7e 3t is dt dy given that…

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Q: Use the Laplace transform to solve the given initial-value problem. y" - y' = e' cos t, y(0) = 0,…

A: GIVEN: y" - y' = et cost

Q: Find dy/dt at t=9 given that y= (u+2)/(u-1), u= (3s-7)2 and s= √t

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Q: Use the Laplace transform to solve the given initial-value problem. y''-y'=et cos(t),    y(0)=0,…

A: Take Laplace transform on both the sides as follows.

Q: Use the Laplace transform to solve the initial-value problem y' + 3y = 13 sin2t, y(0) = 6

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Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: Use the Laplace transform to solve the given initial-value problem. dy -y = 1, y(0) = 0 dt y(t) =…

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Q: 4) Let T=xy ln (x2+y=]; X=e'cosu Cosu, y= e sin u. Find dT, at lu,ul= ( "B,0) at (u,u)= ( "/½ ,0)

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Q: y(T) dr = 4e' cos(2t) COS

A: The solution is given as

Q: dy Use Laplace transforms to solve the initial-value problem dt + 2y = 46(t – 1), y(0) = 1, where &…

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Q: Use the Laplace transform to solve the initial value problem. y''+ 36y = sin(6t), y(0) = 1, y'(0) =…

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Q: y" + 2y' + y = te24 , y (0) = 1, y' (0) = 0 -2t

A: To solve the above differential equation we use the partial fraction and table of Laplace transform.…