Question 6 (30 points Solve the initial value problem. y"+8y + 16y = 0, y(0) =...
Solve the initial value problem y" + 8y' + 16y = 0, y(-1) = 2, y' (-1) = 5. Equation Editor Common 2 Matrix o @ sin(a) seca) s in-(a) cos(a) csca) cosa tan(a) cota) tana) Va Va la U yt) =
(2 points) Consider the initial value problem y' +8y +41y = g(t), y(0) = 0, y(0) = 0, where g(t) = if 9 t<oo. 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() 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...
Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y = 8, 7(0) = 1, y'(O) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) y = 8 Find a linear differential operator that annihilates the function g(x) = 8. (Use D for the differential operator.) Solve the given initial-value problem. Y(X)...
(1 point) Use the Laplace transform to solve the following initial value problem: y! -8y + 20y = 0 y(O) = 0, y (0) = 2 First, using Y for the Laplace transform of y(t), i.e., Y = {y(0), find the equation you get by taking the Laplace transform of the differential equation 2/(s(2)-8s+20) =0 Now solve for Y(s) = 1/[(9-4) (2)+(2)^(2)) By completing the square in the denominator and inverting the transform, find y() = (4t)sint
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" + 8y = 2 - 6, y(0) = 0, y' (O) = -2 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(S) =
Solve the initial value problem below using the method of Laplace transforms. y''+8y'+15y=594e^(6t) ,y(0)=-4,y'(0)=78
Solve the following second order initial value problem by the method of undetermined coefficients: y'-8y' +16 y = 2e", y(0)=1, y'(0)=0.
having trouble finding y(t) NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3, /(0)-9. 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). (s 2Y(s)-3s-9)+16Y(s) help (formulas) 48/s 2 b. Solve your equation for Y(s). C{y(t))=48/(s 2(s2+ 16)...
Page 2 T Use the Laplace Transform method to solve the IVP 1-8y + 16y-te (0) = 1,0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {v}(s), by first moving the expression of the form -as -b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y(8) which will be of...
Problem 3 Solve the initial value problems using Laplace Transforms (a) y' + 8y = t2 y(0) = -1 (b) y" – 2y' – 3y = e4t y(0) = 1, y'(0) = -1