Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" +...
4. Solve the following differential equation by using Laplace Transforms. Y" + 2y' +y = 0, y(0) = 0, y'(0) = 1
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}| find the equation you get by taking the Laplace transform of the differential equation = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =
4. Solve the given differential equation (i.e., find y(t)) using Laplace transform method: and subject to the conditions that yo) = 0 and y” + 2y'+y=0 y’0) = -2. 21
differential equation with Solve the following given initial conditions using the Laplace transform. y" +Sy't by : 4 (t-1)-8(+-2) y 10) = -2 y 10) =5 and
Solve the following differential equation with given initial conditions using the Laplace transform. y" + 5y' + 6y = ut - 1) - 5(t - 2) with y(0) -2 and y'(0) = 5. 1 AB I
y(t)=? Solve the following differential equation by Laplace transforms. The function is subject to the given conditions. y'' +81y = 0, y(0) = 0, y'(0) = 1 Click the icon to view the table of Laplace transforms. y = (Type an expression using t as the variable. Type an exact answer.)
Using the Laplace transform, solve the partial differential equation. Please with steps, thanks :) Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t 2 0. Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t...
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
Use Laplace Transforms to solve the differential equation with initial conditions. 16. y' + y=sin x, y(O) = 1.
(6 points) Use the Laplace transform to solve the following initial value problem: y" + 3y' = 0 y(0) = -3, y'(0) = 6 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 = = + Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) where a <b Y(S) B s+b sta + Now...