If I wanted to solve this [itex] y''+3iy'+y=cos(2t) [/itex] using undetermined coefficients.(adsbygoogle = window.adsbygoogle || []).push({});

and I make the guess [itex] y=Ae^{2it} [/itex]

then i find y' and y'' and then solve for A. I get that A=-1/9

then I take the real part when I multiply it to Eulers formula.

But when I plug this back in to check it doesn't work.

Is there something weird going on because I have an imaginary coefficient in front of the y'.

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# Solving an ODE

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