
5.Solve the initial value problem y" +5y' +6y-g(t), y(0) 0,(0) 2, where (t)-t 1<t<5,. 1, 5 < t. Then sketch the graph of the solution. (Use technologies. Be sure the graph is neat.) Sec. 7.6.39]
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
Solve: Y'” – 134"' + 654' – 125y = 0 y(0) = 3, y’(0) = 19, y''(0) = 87 g(t) = Preview
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Solve y"' +94 = 0, v(65) = - 1, x' (65) = 9 g(t) = Preview The behavior of the solutions are: Steady oscillation Oscillating with increasing amplitude Oscillating with decreasing amplitude
if t < 41 8(t) = 41 if t > 41 Solve the differential equation y(0) = 6, 7(0) = 5 y" +4y = g(t), using Laplace transforms. ift < 41 if t > 411
Solve: y' – 4y' + 3y = 9t – 3 y(0) = 3, y'(0) = 13 y(t) = Preview
Problem 5: Solve the initial valuc problem using Laplace transforms "+3'+2y g(t), with initial conditions y(0) 2 and y (0)-1 were (2, for 1<t 2 g(t) - 0, for 0<t<1 and t >2
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6