d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

Q: у" +у%3D0.001t?, У (0) %3D 0, у'(0) %3D 1.5

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Q: 1 -s F(s) = e = -+ s2 e-3s

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: Example 7.5 Determine the Inverse Laplace Transform of the following expressions using Partial…

A: We use the table of Laplace transform to solve the given question.

Q: Exercise: 5 a) Find the outward flux of the vector field F(x, y, z) = x³i + y³j + (z³ + xz)k across…

A: Given the vector field  Fx,y,z=x3i+y3j+z3+xzk and z=a2-x2-y2

Q: -t yい-yle1-224) yloloo, y'lo).3

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Q: t¢ (0, 5 te (0, 5 æ' (t) + 3.x (t) = f (t), x (0+) = -2, ƒ (t) = 10 sin t

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Q: f(d) = e-2d d4

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Q: y" + 2y' + 5y = 10e¬2", y(0) = 0, y'(0) = 0.

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Q: t3 - 3t2 + 5t – 8

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Q: y" + 3y/ + 2y = e-t, y(0) = 0, y'(0) = 2.

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Q: Find the Laplace transform of the given periodic function 0<t<1 f(t) 1<t< 2

A: Given ft=00&lt;t&lt;1t1&lt;t&lt;2

Q: y" + y = -2 sin t + 10 8(t – 7), y(0) = 0, y'(0) = 1.

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Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 5r…

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Q: Solve the equation subject to the given conditions. d'y dy dx² dx 6y=4, y(0)=3, y'(0)=2

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Q: a"(t) + 16x(t) = 5 sin t, a'(0) = x(0) = 0 %3D

A: First we have to take Laplace transform of the given equation.

Q: 5 sinh (3t) +4 cosh (3t)

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Q: Solve the laplace transform 3x-6x= Sin 2t %3D given when t=0

A: Use the laplace transformation table and derivative formula

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y (1) =…

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Q: e. dt2 d²y dy + 4y = 8t – 10, y(0) = 1, y'(0) = 7 dt f. 3- dy 3– 2 - y = 2y – 1, y(0) = 7,y'(0) = 2…

A: Since you have posted multiple question and according to guidelines we will solve only one question.…

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

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Q: Solve the initial value problem using the Laplace transform.

A: Given initial value problem is y'''(t)+5y''(t)+9y'(t)+5y(t)=t2ety(0)=0, y'(0)=0, y''(0)=-2…

Q: x" (t) – x' (t) = te*, x (0+) = 1, x' (0+) = 0. --

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Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: Find the Laplace transform of the following signal which is periodic with period 20. 20 15 20 t -201

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Q: Q18: y′ − 2y + [y(2) dz=e², y(0) = 0.

A: The given equation is         y' - 2y + ∫0tyzdz = et  . . . . . . (1)     With condition y(0) = 0 .…

Q: Solve the initial value problem using Laplace Transform

A: As per the question we are given the following second order homogeneous linear differential equation…

Q: y" - 4y' + 4y = cos(t); y(0) = 1, y'(0) = -1

A: Given:The initial value problem is given by,                To Find:We have to solve the given…

Q: Laplace solves the Initial Value Problem Find by transform.

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Q: y" +y = 8(t- 2m), y(0) = 0, y'(0) = 1 %3D

A: