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7. Use the method of Laplace transform to solve ty" +2(2t - 1)y' +4(t – 1)y...
Apply the Laplace transform to the differential equation, and solve for Y(s) y'25y 2(t 4)u4(t) 2t 8)us(t), y(0) = y'(0) = 0 Y(s) = Preview syntax error Apply the Laplace transform to the differential equation, and solve for Y(s) y'25y 2(t 4)u4(t) 2t 8)us(t), y(0) = y'(0) = 0 Y(s) = Preview syntax error
[15] 9. By using the Laplace transform method solve the initial value problem -2t y" – 2y' + y = e 7 y(0) = 0, y'(0) = 1.
Use the Laplace transform to solve the initial value problem: y' + 4y = cos(2t), y(0) = 0, y'(0 = 1.
7.(9pts) Solve the initial value problem by the method of Laplace transform: y"+ y = u(t - 3), y(O) = 0, y'(0) = 1.
2. a) Use the Laplace transform method to solve: y" + y' + 1.25 y = t - UT y(0) = 0, y'(0) = 0. b) Draw a careful graph of the forcing function in this mass-spring-damper problem. c) Using a computer or calculator construct a careful graph of the function.
7 Question Six: (5 marks) Solve the following integral equation using the Laplace transform. y(t)-/ sin(2t)y(t-r)dr-3. 0
5. Use the Laplace transform to solve the problem 2t y" + 3y' – 4y e2, = y(0) = 0, y'(0) = 0.
solve 2y''(t)+ty'(t)+y(t)=0 with laplace transform using error functions (the previous question was find the laplace transform of e^(-t^2) ), also we may assume when s goes to infinite, Y(s) = 0 I find out that Y(s) = 2 integral(e^(-s^2)) / e^(-s^2), but i cant calculate this :( (maybe using convolution?)
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
solve the following using laplace transform y" + 4y + 4y = t4e-2t; y(0) = 1, y'(0) = 2 +