(1 point) Since 8t2 sinh(at) + 5+ sin(at) = ť? (8 sinh(at) + 5 sin(at)). to...
(1 point) Find the Laplace transform of 7emt – 6t3: (1 point) Since 3temt – 7t2 sin(at) = {2 (3emt – 7 sin(at)), to find the Laplace transform of 3t2 emt – 7t+ sin(at) you take the second derivative of Therefore L{3t2 emt – 7t2 sin(at)}(s) =
Find the derivative of the following: f(x)=( Sinh(Sin-(x2)))3 оа. Select one: - 6X(Sinh(Sin-(x^))) Cosh(Sin-1(xº) √1-8" 3(Sinh(Sin-'(x2)))?Cosh(Sin-'(x2)) O b. 71-X 3(Sinh(Sin '(x2))) Cosh(Sin ?(X)) O c. 71-X 6XCosh(Sin-'(x?)) O d. V1-14
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) = 4. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 8/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = c. Take...
(1 point) a. Find the Laplace transform F(s)-f(t)) of the function f(t)-7+sin(2t), defined on the interval t 0 F(s) = L(7 + sin(2t)) = help (formulas) b. For what values of s does the Laplace transform exist? help (inequalities)
(1 point) Solve the boundary value problem by using the Laplace transform: 4 ²w дх2 d²w at2 ? x > 0, t> 0 w(0,t) = sin(8t), lim w(x, t) = 0, t> 0, X00 W(x,0) = 0, dw -(x,0) = 0, x > 0, дt First take the Laplace transform of the partial differential equation. Let W be the Laplace transform of w. Then W satisfies the ordinary differential equation W" = subject to W(0) = and limx→ W(x) =...
(1 point) Consider the initial value problem 4y 8t, y(0) 4, y'(0) 3. f both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from othe other (until you get to part (b) below). Take the Laplace transform one side of the equation help (formulas) b. Solve your equation for Y(8) Y(s) C{y(t) = Take the inverse Laplace transform of both sides of the...
The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its applications. (The hyperbolic cosine, for example, describes the curve of a hanging cable, called a catenary.) They are defined by the conditions cosh(0)-l, sinh(O), (cosh())inh("), d(sinh()- csh) (a) Using only this information, find the Taylor polynomial approximation for cosh(x) at0 of COS degree n = 4. (b) Using only...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
Please show work! (1 point) Find the Laplace transform F(s) of f(t) { O, t<6 5 sin(at), 6<t<7 0, t> 7 F(8)
(1 point) Take the Laplace transform of the following initial value problem and solve for Y(8) = L{y(t)}; ſ1, 0<t<1 y" – 6y' - 27y= { O, 1<t y(0) = 0, y'(0) = 0 Y(8) = (1-e^(-s)(s(s^2-6s-27)) Now find the inverse transform: y(t) = (Notation: write uſt-c) for the Heaviside step function uct) with step at t = c.) Note: 1 | 1 s(8 – 9)(8 + 3) 36 6 10 + s $+37108 8-9