Consider the following initial value problem. y" + 8y' + 25y = 8(t – n) + 8(t – 7x), y(0) = 1, y'(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7ts -TS + e + (s + 8) (s + 4)2 + 32 e L{y} = Use the Laplace transform to solve the given initial-value problem. A(a-)sin 3(t – 1) x )· «(t - «) + ( \ e-^'cos(3t) × )- a( - 4 -4t 'e sin (3t) | × 3 y(t) = t - n) + 3 7n

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

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A: So, we will have to use [ RL ]0  as a value in here, and hence, it will be treated as a constant.…

Q: Consider the following initial value problem. у" + 8y' + 25y %3D 8(t — п) + 8(t - 7л), у(0) 3D 1,…

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A: As per our guideline we can solve only first three subparts.Please repost for another question.…

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Q: y(t) = y" - 7y' + 6y = et + s(t - 7) + 6(t-9), y(0) = 0, y'(0) = 0 ) + ( [ ])2(x-7)+ ( [ 1) 2(t-1

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Q: 2- Solve the fractal differential equation Day + y = 5e²x With a = a = and and y(0) = 1, Using…

A: Given Fractal Differential Equation:  Where ​ and .Objective: To solve the given fractal…

Q: . Determine the Laplace transform of the differential equation 3y" – y' = et5 - 9y" + 4y

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A: Given differential equation is