2.5. y"yuT/2 (t) 8(t-) - u3/2(t); y(0) = 0, y'(0) = 0 2.6. y" 2y 2y...
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:
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Solve the Following: 2y'' + y'+ 2y = u5(t) − u20(t) y(0) = −1 y 0 (0) = 3
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
Solve, using Laplace Transforms: Y" + 4y = ui(t) - u3(t), y(0) = 1; y'(O) = 0
2-8 Derive Equations (2.6) and (2.7) 0 1 (2.6) sin 0 0 cos0 O sin 0 cos O sin Cos (2.7) Ry.8 0 0 1 - sin 0 cos e 0 l
(25pt| 3. Find y(t) if x(0) = 0 2 + 2y + u(t), 2.r + y, y(0) = 2 where it is the unit step function.
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
Find the solution of the initial value problem y" – 2y' + 5y = g(t), y(0) = 0, y'(0) = 0, where g(t) is a continuous, otherwise arbitrary, function. Oy(t) = g(t) 1 y(t) = (sets sin(2t))g(t) Oy(t) = (cos(2t)) * g(t) Oy(t) = (cos(2t))g(t) y(t) = (1 e*) + f(t) x(t) =() e sin(26)g(t) g(t) = ( e sin(2t) + (t) y(t) = Ce+ sin(2t)) *g(t) 1
4. Find the solution to the differential equation y"+2y'+ 2y-S(t-) y(0) 0, y (0)-0 and graph it.