2. Use the Laplace transform to find a particular solution of the differen- tial equation (as...
Q4 please 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks] 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
Question 1: [25 pts] S+1 a) Find the inverse Laplace transform of the expression $2+4 b) Find the inverse Laplace transform of the expression (s-5)(s2+4) c) Use the information from the parts a) and b) to find the solution of the IVP y" + 4y = 6e5t, y(0) = 1, y'(0) = 1.
Use the Laplace transform to find the solution to the differential equation y'' + y = U(t − 1), y(0) = 1, y' (0) = 0. Describe the physical system that this differential equation represents. Plot your solution.
could someone explain this with helpful workspace? Problem 3. (1 point) Use the Laplace transform to solve the following initial value problem: y" +9y' = 0 y(0) = 3, y(0) = 5 a. 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 b. Now solve for Y(S) = c. Write the above answer in its partial fraction decomposition, Y(s) = sta +...
I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
I need help with this question of Differential Equation. Thanks Find the Laplace transform Y(s) = [{y} of the solution of the given initial value problem. 1, 0 <t <t y" + 4y = to, a st<co y(0) = 8, y'(0) = 7
Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. St, 0<t<1 y" + 4y = {i;isica , y0 = 8, Y' (0) = 6 Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (3) = QE
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a 2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a
Use the Laplace transform to find y (t), a particular solution, in each of the systems shown te-PuO) e-ul)
Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3t), y(0) = 0, y(0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. 3s L{y(t)}(s) = (452 + 25 +2s + 18)(52+9) b. Express the...