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.

calculus ordinary-differential-equations derivatives
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