Let Solve the differential equation using Laplace transforms. y(t) = t/16+5cos(4t)+95/64sin(4t) g(t) = { y" + 16y = g(t), if t < 8T 8π if t > 8π y(0) = 5, y'(0) = 6 if t < 8T if t > 8T

Q: Transform the differential equation -2y + 4y = cos(at) y(0)=-6 into an algebraic equation by taking…

A: The differential equation is: -2y'+4y=cosat; y0=-6. We have to transform the given differential…

Q: Solve the differential equation using Laplace transform of y" - 3y' + 2y = e3t ; when y(0) =0 and…

A: To Solve: y''-3y'+2y=e3t; when y0=0 and y'0=0 Concept: Let Lyt=Ys be any given Laplace TransformThen…

Q: Show that the transformation z = log tan (x/2) reduces the differential equation d²y +cotr +4x…

A:

Q: Employ Laplace transforms to solve the differential equation of y"-2y'+y=3e¹* Given y(0)= and y(0) =…

A:

Q: Consider the differential equation 2y" + ty' - 2y = 18, y(0) = y'(0) = 0. In some instances, the…

A: Given differential equation is 2y''+ty'-2y=18 Also given y0=y'0=0   To Solve: The first-order DE for…

Q: Show that w(t) =〈sin(3t + 4),sin(3t − 2)〉, cos 3t satisfies the differential equation w''(t) =…

A: Given- wt=&lt;sin3t+4,sin3t-2&gt;,cos3t To prove- That the above expression satisfies the…

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

A:

Q: Consider the following initial-value problem. y' - y = 2 cos(4t), y(0) = 0 Find {f(t)} for f(t) = 2…

A: Solution :-

Q: the ential equation 2y" + ty'- 2y 14, y(0) = y'(0) = 0. n some instances, the Laplace transform can…

A: In the given question, concept of laplace Transform is used. Laplace Transform The Laplace transform…

Q: Consider the following initial value problem: x" – 2x' – 24x = sin(7t), x(0) = 5, x'(0) = -1. Using…

A: Given differential equation is

Q: Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an…

A:

Q: Consider the following initial-value problem. y' - y = 2 cos(3t), y(0) = 0 Find L{f(t)} for f(t) = 2…

A:

Q: Answer the following questions and show all of your work. (a) Sketch the following function where…

A: The Laplace transform of the function f(t) is given by L[f(t)]=∫0∞e-stf(t)dt. Since the dimension of…