Solve the ODE d²c dt² - 4 d = dt +4 -2C at C(0)= dc dt 1

Q: Let r(t) = Find f(t)dt ( )dt (don't include the +C) fF(t)dt = <[ Calculator 1 Check Answer

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Q: df + At" f(t)– B•cos(@t) dt with A = 5, n = 2, B = -6, w = 12, and f(0) = 3. derive an expression…

A: We are given the differential equation,                                      .

Q: Find a linear differential operator that annihilates the given function 1+6x-4x3

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Q: tan (Int) dt

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Q: - (7)f | dt, then f (z) 1.

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Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: How do you evaluate ∫ba r(t) dt?

A: Consider the given: ∫abr(t)dt Consider the first fundamental theorem of calculus: Let r(t) be…

Q: [2 0 -1 2 1] В — -1 1. Let A 3 1 [1 2 D = C = E = -1

A: DA  = 21112310-12        = 2×2+1×0  2×3-1×1  2×1+1×21×2+1×0  1×3-1×1  1×1+1×2        = 454223 (DA)'…

Q: Determine the intervals where F is concave up and down. (Give your answer as an interval in the form…

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Q: Sketch the bifurcation diagram for the ODE dx dt = rx + x³,

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Q: (0.52)* ) 1 1+x²

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Q: Let f (x) = dt. Find the value of f'(2) 4 -12 8 -24 -4 24 12 -8 100

A: Newton's Leibnitz rule for one variable is as, I(x)=∫ϕ(x)ψ(x)f(t)dtdI(x)dx=f(ψ(x))ψ'(x)-f(ϕ(x))ϕ'(x)…

Q: Solve the first-order linear ODE t(t + 1)x' + tx = 6.

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Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: Given equation d² x 1 dx + dt² - t dt t- d²x dx + = t³ (x) 4 dt² dt d dt [tx] = t³ (x¹) d(tx) dt…

A: Here, we explain all steps that have been done in given question .

Q: Let f(x) = 1 + x³ + dt. Determine the value of (f-1)'(0).

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Q: ++Xt+1)dt

A: b) The given integral is ∫t+1t+1dt