(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I took differential eq-n class more than a year ago and I am having problem solving this problem.

5(d^3y/dt^3)+3(d^2y/dt^2)+7(dy/dt)+y = 4(d^2f/dt^2), where f(t)=cos(t)-2sin(t)

2. Relevant equations

none

3. The attempt at a solution

First thing I did was to take the second derivative of f(t) and multiply it by 4 for the right side of the equation, which turns out to be 4(-cos(t)+2sin(t))=-4cos(t)+8sin(t).

For the left hand side, I take its characteristic equation 5y^3+3y^2+7y+1=0 and tried to solve for the roots of the cubic equation, but turns out the roots are not whole & real numbers:

t1 = -0.15009708847612485

t2 = 0.22495145576193756+1.1321959748355932i

t3 = 0.22495145576193756-1.1321959748355932i

Then I am not sure how to proceed... or did I use a wrong approach? If not then how should I proceed the problem with what method? (undetermined coefficients?) Not sure if this helps, this differential equation describes a circuit with y(t) as the output and f(t) as the input. I was asked to find the steady-state output of the circuit. So I figure I should take the limit of the solution of the differential equation as t approach infinity.

Any help will be appreciated!

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# Homework Help: 3rd order differential equation

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