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2.14. For each differential equation given below, find the solution for t 2 0 with the...
Find the general solution of the following non-homogeneous differential equation d 2 y dt2 + 2 dy dt + y = sin (2t). (2) Now, let y(t) be the general solution you find, when happen if we take lim t→+∞ y(t)? 2. Find the general solution of the following non-homogeneous differential equation dy dy sin (2t) (2) 2 +y= dt dt2 Now, let y(t) be the general solution you find, when happen if we take lim y(t)? t-++oo
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
Solve the following differential equation using variation of parameters. d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3 d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3
II. Find the solution of the differential equation that satisfies the given initial condition du 2t +sec2 t dt 2uu(0-5 di 1. 2·y' + y tan x = cos2 x, y(0) =-1 dy 6. ( In,() 10
For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t) 9 dt y(t) 5x(t) 7 2 6 dt3 dt2 dt2 Express the system transfer function using the pole-zero plot technique a) b) What can be said about the stability of this stem? For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t) 9 dt y(t) 5x(t) 7 2 6 dt3 dt2 dt2 Express the system transfer function using...
find the general solution of the differential equation by using the system of linear equation. please need to be solve by differential equation expert. d^2x/dt^2+x+4dy/dt-4y=4e^t , dx/dt-x+dy/dt+9y=0 Its answer will look lile that: x(t)= c1 e^-2t (2sin(t)+cos(t))+ c2 e^-2t (4e^t-3sin(t)-4cos(t))+ 20 c3 e^-2t(e^t-sin(t)-cos(t))+2 e^t, y(t)= c1 e^-2t sin(t)+ c2 e^-2t(e^t-2sin(t)-cos(t))+ c3 e^-2t(5e^t-12sin(t)-4cos(t))
3. (30 points). Determine function y(t) from the following differential equation using the Laplace transform d?y dt2 dy. +42 + 3y = 3 dt y(0) = 2, y'(O) = 0
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
(1 point) a. Consider the differential equation: d2y 0.16y-0 dt2 with initial conditions dt (0)-3 y(0)--1 and Find the solution to this initial value problem b. Assume the same second order differential equation as Part a. However, consider it is subject to the following boundary conditions: y(0)-2 and y(3)-7 Find the solution to this boundary value problem. If there is no solution, then write NO SOLUTION. If there are infinitely many solutions, then use C as your arbitrary constant (e.g....
(a) Find the general solution of the following second order linear differential equation given that y1 = t is known to be a solution: t2y" - (t2 + 2t) y' + (t + 2)y = 0, t> 0. (b) Find the particular solution given that y(1) = 7 and y'(1) = 4.