Use Laplace Transform to solve the following Differential Equations: d) dy + 4y = 2e –...
Use the Laplace transform to solve the given system of differential equations. Use the Laplace transform to solve the given system of differential equations. of + x - x + y = 0 dx + dy + 2y = 0 x(0) = 0, y(0) = 1 Hint: You will need to complete the square and use the 1st translation theorem when solving this problem. x(t) = y(t) =
differential equations Use the Laplace transform to solve the given initial-value problem. y" - 4y' + 4y = 6%e2t, y(0) = 0, y'(O) = 0 y(t) =
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.
2. Using Laplace transform, solve the system of differential equations d.x: dy dt where x(0)1 2. Using Laplace transform, solve the system of differential equations d.x: dy dt where x(0)1
use the Laplace transform to solve the given system of differential equations dx dt dx dt dt dt x(0) 0, y(o)0 x(t) =
Solve the following differential equation. Do not use Laplace. y'' – 4y' = 2e (2x+3) - Write the corresponding homogeneous equation and find the homogeneous solution. - Find the particular solution using the non-homogeneous differential equation. - Finally write the general solution.
Use Laplace Transform to solve the following Differential Equations a) y - 2 sin(5t) = y, y(0) = 0
Use the Laplace transform to solve the given system of differential equations.$$ \begin{aligned} &\frac{d x}{d t}=x-2 y \\ &\frac{d y}{d t}=5 x-y \\ &x(0)=-1, \quad y(0)=5 \end{aligned} $$
Solve the system of differential equations using Laplace transformation dx dy dt - x = 0, + y = 1, x(0) = -1, y(0) = 1. dt You may use the attached Laplace Table (Click on here to open the table) Paragraph В І
Use Laplace Transform to solve the following Differential Equations b) y'' +9y x?, y(0) = 0, y (0) = 0.