Solve for Y(s), the Laplace transform of the solution y(t) to the initial valu y" + 5y = g(t), y(0) = -1, y'(0)=0, where g(t) = { t, t<3 1, t> 3
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- Solve the initial value problem below using the method of Laplace transforms. w'' - 4w' + 4w=24t+28, w(-2)= -2, w'(-2) = 5 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.3. (a) Calculate the Laplace transform of each function. Explain your reasoning (i) cos(2t) sin(4t). (ii) est cosh(3t). (iii) H(t-2) sin(4t-8). (iv) (t-3)²e-2tH(t-3).b) Using the table of standard transforms, find the Laplace transforms of the following functions: (i) 6e-²t cosh(5t) (ii) t² e ³t
- Find Fourier transform for the following functions:x(t)=3+(sin2wt)2Apply the translation theorem to find the inverse Laplace transform of the following function. F(s) = %3D 2s - 16 Click the icon to view the table of Laplace transforms. L-^{F(s)} =O (Type an expression using t as the variable.)Solve (i) and (ii) using Laplace transform
- Solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution. w''+w=2u(t-3)-u(t-4); w(0) = 2, w'(0)=0 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.Solve the following equations show your solutions. 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1). 2. Find the area of the circle with center at (1, 3) and tangent to the line 5x - 12y - 8 = 0. 3. Determine the Inverse Laplace Transform of F(s) = (s + 2)(e^-s)/(s^2 + 4).(ii) -2t L[e Find the Laplace transform of sin2