Use the Laplace transform to solve the given initial value problem. \[ y'' + 2y' + 5y = 0; \quad y(0) = 6, \quad y'(0) = -1 \] \( y(t) = \) [Text Box] There is also an interactive button labeled "GO Tutorial" which presumably provides additional guidance or solutions related to solving the problem using the Laplace transform method.

Q: Use Exact, Then solve (1 = In(x) +)) = (1 – In(x))y`

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Q: Q(0)=135 Q'(t)=k(Q-70) Calculate Q at t=1 second and k=-8/second

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Q: (a) By inspection, find a particular solution of y" + 2y = 14. Yp(x) 11

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: For the function f(x) = 5x° - 3x + 2x + 7x + 3, find f"(x), the third derivative of f, and f4) (x),…

A: Third and Fourth derivative of f(x): f3x=300x2-74x+12f4x=600x-74

Q: A dilation T sends A = (2,3) to A’ = (5,4), and it sends B = (3,−1) to B’ = (7,−4). Where does it…

A: We have, A dilation T sends A = (2,3) to A’ = (5,4) and it sends B = (3,−1) to B’ = (7,−4) Where…

Q: 3. y = In(sec(In 0)) Find the derivation

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Q: Let exy - x3 = y5. Find Y. dy xp O yexy – 8x7 xexy - 5y4 8x7 xexy yeY -5y 5y4 xey - 5y 5y4 8x7 -…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Find the first and second derivatives of the function. 16 L(t) = 1+2.leS L'()=-16(1+2.1*)*(2.10*)…

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Q: Calculate the derivative of the function r(t) i+ cos' (61)j + lIn (2t³)k. t - 2

A: Given : r(t)=-5t-2 i +cos-1(6t)  j +ln2t5 k We have to calculate the derivative of the given…