1. For a non-homogeneous, linear, 2nd order DE, using the method of undermined coefficients, what do you use for the particular solution for [itex]e^x[/itex] and [itex]cosx[/itex] or [itex]sinx[/itex]. For example, if it is [itex]x^2[/itex], you use [itex]Ax^2+Bx+C[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

2.For [itex]y''-2y'+2y=0[/itex] i put [itex]y(x)=c_1e^{(1+i)x}+c_2e^{(1-i)x}[/itex] but got it wrong. The right answer was written as [itex]y(x)=e^{ix}(c_1cosx+c_2sinx)[/itex]. I always assumed that an answer using [itex]e^x[/itex] was right. How do I know when to use [itex]e^x[/itex] and when to use [itex]sinx[/itex] or [itex]cosx[/itex]?

Thanks a bunch!!

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# A couple questions

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