7. Give a linear constant-coefficient differential equation that has general solution y(t) = {2+ + sin(2t)...
Give a linear constant-coefficient differential equation that has general solution y(t) = e 2t + sin(2t) + c1e t + c2tet + c3e −t 7. Give a linear constant-coefficient differential equation that has general solution y(t) = {2+ + sin(2t) + let + Catet + cze-t
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))
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
(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.
Find a constant coefficient linear second-order differential equation whose general solution is: y=(c1 + c2(x))e^-3x
2. (e) (7 points) Find a homogeneous linear differential equation with constant coefficients whose general solution is y = 4 + ce?* + Gxe7x.
Find the general solution of the differential equation: y'−4y=te^−2t Use lower case c for the constant in your answer.
Find a general solution to the differential equation. 1/2y" +2y=2 tan 2t-1/3e2t The general solution is y(t) = _______
QUESTION 7 A solution of a homogeneous differential equation with constant coefficient is given by y = Ae-3* +Bsin 4x +Ccos 4x. Determine the a) order and the roots of the equation. (3 marks) b) differential equation. (3 marks)
Suppose you are solving a linear homogenous differential equation. State the general solution for each of the following situations. You may assume that the dependent variable is y, and y = y(t). a. Second-order constant-coefficient equation, with auxiliary equation roots r = -2 +V-49 b. Second-order constant-coefficient equation, with auxiliary equation roots r = -2 + 149 c. Second-order Cauchy-Euler equation, with auxiliary equation roots r = -2 EVO d. Fourth-order constant-coefficient equation, with auxiliary equation roots r = -6,...