Compute X(s) = L[x](s) where x(t) is the solution of the initial-value problem x''' + 25x' = 24 sin(3t) ;  x(0) = 0 ; x'(0) = 0 ; x''(0) = 0 :

Q: 5. Suppose f(g(x)) = 4x/(x+ 1), and that 8(1) = 2 g'(1) = 1/4 8(2) = 3 g'(2) = 1/6 8(3) = 4 g'(3) =…

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Q: 4. Solve the particular solution of y" + 3y' + 2y = 6e¬, y(0) = 1, y'(0) = 2, using a. Variation of…

A: we have given the differential equation y"+3y'+2y=6e-ty(0) = 1, y'(0) =2 we have to find the…

Q: 1. Indicate whether h(x), h'(x) and h"(x) are positive (+), negative (-) or equal to zero (0), at…

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Q: 3. Find the value(s) of k for which y = e satisfies the equation y+2y' = y" derivative) (note: y" is…

A: k = 1+2, 1-2explanation is given in below step

Q: Solve the Initial value problem x' -x=8(t-2),x(0) =x' (0) =0

A: We use the Laplace transform to solve the given initial value problem.

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

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Q: An object with mass m = 1 kg is attached to a spring with spring constant k and a dashpot with c =…

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Q: a) If F(x) = f(g(x)), where f(−1) = 9, f '(−1) = 5, f '(1) = 3, g(1) = −1, and g'(1) = 8, find F…

A: Note to student :  This question have 4 sub questions. As per our Bartleby Guidelines, we are only…

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: Solve (1 07 y'' – 4y' + 3y y(0) = y'(0) = 0 y(t) = f(t)uo(t) - g(t)u7(t), where f(t) = g(t) =

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Q: (a) State the definition of the 'usual' differential of a function F(x). (b) Use the relation F(x +…

A: Definition of the differential function of F(x):   Part (a):   Let the function F(x) is continuous…

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: 5. Consider the equations: det f(x) = A(1+)™* g(x) = A· ex and %D %3D For x =1 (a one year…

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Q: 6 3 Find h'(t) if h(t) = 5/6 ¯ ,1/5

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Q: 0 -2 5 3 2 3 1 -1 -2 4 (a) If h(x) f (x) find h'(0). g(x)' (b) If m(x) = In(S(x)), find m'(3).

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Q: z(x) 1+x² You need to find the formula for y'(x) first, then evaluate y'(x) at x = (c) Let y(x) = =…

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Q: Solve the equation x" +2x'+2x=25(t-π), x(0)=0, x'(0)=0 a. x(t)==—=sin(2t) x(t)=[1-e-²¹-2te-²¹] +…

A: Given differential equation

Q: 3. Determine the general solution to the equation xy' = (1+ x) sec(y), x > 0. You can leave your…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.