Hi I have problem to answer this question. I think that it is a question of recognizing the right solution rather than computing.(adsbygoogle = window.adsbygoogle || []).push({});

Give the general solution of the differential equation:

y'' -6y'+9y=-5e^{(3x)}+(1/x)e^{(3x)}

1- y=C_{1}*e^{(3x)}+C_{2}*x*e^{(3x)}-(5/2)x^{2}*e^{(3x)}+x*e^{(3x)}*ln(x)

2- y=C_{1}*e^{(3x)}+C_{2}*x*e^{(3x)}-(5/2)x*e^{(3x)}-x*e^{(3x)}*ln(x)

3-y=C_{1}*e^{(3x)}+C_{2}*x*e^{(3x)}-(5/2)*e^{(3x)}+e^{(3x)}*ln(x)

My problem is when to know if the particular solution is multiply by x or x^2.

when the particular solution is a solution of the homogenous equation , we multiply the particular solution by x. when do we multiply by x^2??

Can you give me a quick example please??

Thank you

B.

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# Homework Help: 2nd ODE

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