Use the Laplace transform to solve the following initial value problem: y" - y' - 20y= 0, (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)). find the equation you get by taking the Laplace transform of the differential equation to obtain (2) Next solve for Y = y(0) 9, y(0) 9 0 A (3) Now write the above answer in its partial fraction form, Y + a B 8-b (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a

Q: c. write the above answer in its partial fraction decomposition, Y(s) = sq + Y(s) = + d. Now, by…

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Q: Use the Laplace transform to solve the following initial value problem: y" - 1y - 30y = 0 y(0) = −4,…

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Q: Consider the initial value problem +16y=48t, y(0)=9, (0) = 5. a. Take the Laplace transform of both…

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A: a)b) c)

Q: When solving a differential equation using the Laplace transform, you apply the Laplace transform to…

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Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: Consider the following initial value problem: y′′−4y′−45y=sin(5t)     y(0)=7,y′(0)=5   Using Y for…

A: The given initial value problem,.We have to find the Laplace function using the Laplace transform.

Q: Use the Laplace transform to solve the following initial value problem: y" – 3y = 0, y(0) = 2, y'(0)…

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Q: Use the Laplace transform to solve the following initial value problem: y" – 7y' + 10y = 0, У(0) —…

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Q: Consider the initial value problem y" + 9y= 18t, y(0) 5, y(0) = 9. = a. Take the Laplace transform…

A: Step 1: Step 2: Step 3: Step 4:

Q: Use the Laplace transform to solve the following initial value problem: y" - 6y - 16y=0 y(0) = 1,…

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Q: In this exercise you will use Laplace transforms to solve the differential equation y"+5y'+6y= 0,…

A: (1)let a and b constants , then L(af(t)+bg(t))=aL(f(t))+bL(g(t)).(2) L(eat)=1s−a

Q: Considel the initial value problem y" – 4y' + 8y = sin(8t) y(0) = 8, y'(0) = 7 A. Use the Laplace…

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Q: L{y(t)} = (s/((s+36)(s^2+36)))+((8+7s)/(s^2+36)) c. Take the inverse Laplace transform of both sides…

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Q: When solving a differential equation using the Laplace transform, you apply the Laplace transform to…

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A: Step 1: Step 2: Step 3: Step 4:

Q: t) Consider the following initial value problem: S 7t, 7t, 0 6 Using Y for the Laplace transform of…

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Q: y(0) = 1, y'(0) = −2 y" + 8y = 0 First, using Y for the Laplace transform of y(t), i.e., Y =…

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