by the technique of undetermined coefficients. So ns need an initial to uncover a solution to the no homogeneous equation. I"m utilizing a to organize that says that I just need to find the services for:

$$y""+y = 3sin(2t)$$and$$y""+y = tcos(2t)$$

and them sum the two solutions. Climate I simply need to amount this final solution with the basic solution because that the homogeneous equation. The problem is that the prize in my publication is the following:

$$y(t) = c_1cos t+c_2sin t-frac1ttcos 2t-frac59sin 2t$$

but I resolved $y""+y = 3sin 2t$ and also got $y=-sin(2t)$, i beg your pardon is exactly according to wolfram alpha, so just how does that $-frac59$ appeared?

Also, which have to be the guess for the equation $y""+y = tcos(2t)$? I"m gonna try $(at+b)(ccos 2t + dsin 2t)$, is that right? due to the fact that the derivatives space huge.

You are watching: Y'+y=3 sin(2t)+tcos(2t)

Please remember that I need to use the method of undetermined coefficients.


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