Solve for the general and particular solution using Laplace Transform y" + y = sqrt (2) (cos sqrt (2)t) y(0) = 10 , y'(0) = 0

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A: (a)     Domain : { -2, -1, 0, 1, 3 }          Range : { -1, 3, 5 , 3, 3 }          Function : Yes…

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Q: 5. Prove that there is no value of k such that the equation æ³ – 3x + k = 0 has two distinct roots…

A: To prove: There is no value of k such that the equation x3-3x+k=0 has two roots in [0,1].

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Q: A s(1) = e-7" sin(8 1) () = e" sin(3 1) © s(1) = e3 sin(7 1) Os() = e-5 cos(71) D

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Q: What is the Laplace transformation of  L{e-2t cosh (4t) + e-2t sinh (4t)}

A: Here we can use the following formula Lcoshat=ss2-a2Lsinhat=as2-a2andLe-atft=Fs+a   where Lft=Fsthe…

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A: y = 3x3+1 , y = 3x + 1

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Q: 3. Suppose we know that the graph below is the graph of the right-hand side f(y) of the differential…

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Q: 88+88

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Q: 8. Solve the given initial value problem. dx = 3x +y- e 3t. x(0) = 2 dt dy = 4x + 3y; dt y(0) = - 5…

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