Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: S sin(nt), 0

Q: 1. Find the instantaneous rate of change when x=π for y=sin*x/2-3cosx.   2. Interpret geometrically…

A: Simply take the derivative and put the given point to find the instantaneous rate of change.

Q: f(t) = sinhtcost

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Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

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Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: Use the Laplace transform to solve the difference equation 3x(t) — 4x(t − 1) = 1, x(t)=0 for t < 0.

A: Given: The difference equation, 3xt-4xt-1=1, xt=0 for t&lt;0   To solve: The given difference…

Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

A:

Q: Find the Laplace transform F(s)=L{f(t)} of the function f(t)=e^(−3t) cosh⁡(5t).

A: Laplace transform of the function, f(t)=cosh(at) is

Q: g (t) = tsin (nt)

A:

Q: f (t) = cos² (πt)

A:

Q: Let A={0,3,4,9,11}A={0,3,4,9,11} ,   B={0,4,9,10}B={0,4,9,10} ,   C={1,3,6,8,9,10} List the…

A: It is given that, A={0,3,4,9,11},  B={0,4,9,10}, C={1,3,6,8,9,10}. Obtain the A∩B as follows.…