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Q4 a) Find the general solution of the differential equation Y') + {y(t) = 8(6+1)5; 8>0....
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
Find the solution for the following differential equation using Laplace transforms: x - x-6x-0, where x(0)-6, x(0) 13 Find the inverse Laplace Transform of the following equation: 547 s2 +8s +25 x(s) =
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
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Find the general solution of the following differential equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? + ?e^(-t). (please solve Question No.7 only) 7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
Use the method of Laplace transforms to find a general solution to the differential equation below by assuming that a and bare arbitrary constants. y'' + 2y' + 2y = 1, y(0) = a, y' (O) = b Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) = 1 (Type an exact answer in terms of e.)
(1 point) Solve the differential equation -1, y (0)2 y-4y -5t263 (t) y(0) using Laplace transforms. for 0 t3 The solution is y(t and y(t) for t> (1 point) Solve the differential equation -1, y (0)2 y-4y -5t263 (t) y(0) using Laplace transforms. for 0 t3 The solution is y(t and y(t) for t>
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.
Given the differential equation y'' – 9y = - ett + 3e8t, y(0) = 0, y'(0) = 4 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Preview Now solve the IVP by using the inverse Laplace Transform y(t) = L '{Y(8)} g(t) = Preview
Please answer parts c-d only. 4. In lab 4 we consider the differential equation y" 2yywyF(t) for different forcing terms F(t). In this problem we analyze this equation further using Laplace transforms 0, t<1 (a) Consider y" + y, +40y-1(t), where I(t)- t < 2. Find 1 1, 0. t>2 the forward transform Y-E(y) if y(0)-y(0)-0 (b) Solve y" + y, + 40y-1, y(0) = y'(0) = 0, using Laplace transforms Notice how the value of Y (s) you obtain...