(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Lapla...
(1 point) Consider the initial value problem d'y dy dt2 dt dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y Write down the Laplace transform of the right-hand side of the equation Your answer should be a function of s only. Next equate your last two answers and solve for Y. You...
1 point) Consider the initial value problem dy 29y--9e cos( dt dt2 dt Write down the Laplace transform of the left-hand side of the equation given the initial conditions Y(sA2-10s+29)+3s-24 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation -9(s-5(S-5)A2+9) Your answer should be a function of s only. Next equate your last two answers and solve...
d2y dy +10 dt +25y 0, y(1) 0, y'(1) 1 (1 point) Solve the initial-value problem dt2 Answer: y(t)
(1 point) a. Consider the differential equation: d2y 0.16y-0 dt2 with initial conditions dt (0)-3 y(0)--1 and Find the solution to this initial value problem b. Assume the same second order differential equation as Part a. However, consider it is subject to the following boundary conditions: y(0)-2 and y(3)-7 Find the solution to this boundary value problem. If there is no solution, then write NO SOLUTION. If there are infinitely many solutions, then use C as your arbitrary constant (e.g....
(Example 7.2.4) Use the Laplace transform to solve the initial-value problem 6. dy + 3-13 sin 2t, dt y(0)-6
(1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.) (1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.)
1 point) Consider the initial value problem y" + 36y-cos(61), y(0)-6 (0)-8, 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). help (formulas) b. Solv e your equation for Y (s) Y(s) = L { y(t)) = c. Take the inverse...
Consider the following initial value problem. y′ + 5y = { 0 t ≤ 1 10 1 ≤ t < 6 0 6 ≤ t < ∞ y(0) = 4 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the...
(1 point) Consider the initial value problem a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of v(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). help (formulas) (sh2+4)Y(s)-(8s+5) Solve your equation for Y(s) b. c. Take the inverse Laplace transform of both sides of the previous equation to solve for...
(1 point) Consider the initial value problem y" + 4y = 81, (0) = 2, 7(0) = 8 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). help (formulas) b. Solve your equation for Y(). Y(s) 1900) c. Take the inverse...