xtra points: Solve the following differential equation with initial condi- tion by using the Laplace transform...
Solve the following differential equation using the Laplace transform and assuming the given initial conditions. [Note: Laplace table is provided in the page 6] dt2 dt dix x(0) = 1 ; (0) = 1 dt
6) a) Solve the following differential equation using the Laplace transform method. dy = 1.87ylt) + 4.05 y0) = 1 You may need the expression, 1.05 4.05 s(s - 1.87) 1.87(s - 1.87) 4.05 1.87s [8 marks] b) Solve the following differential equation using the Laplace transform method. dºy + 2.61X + 6.55y(t) = 0 y(0) = 1, y'(0) = 1 2. You may need the expression, s +1 +2.61 52 +2.615 +6.55 *2.01.2015 - | 1+2,61 (8+2.01) + ((6.55-...
3. (30 points). Determine function y(t) from the following differential equation using the Laplace transform d?y dt2 dy. +42 + 3y = 3 dt y(0) = 2, y'(O) = 0
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
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
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
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
(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) =
(6 points) Use the Laplace transform to solve the following initial value problem: y" – 10y' + 40y = 0 y(0) = 4, y'(0) = -5 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) By completing the square in the denominator and inverting the transform, find y(t) =
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...