solve the initial value problem:(adsbygoogle = window.adsbygoogle || []).push({});

y^{''}+8.4y^{'}+17.64y=e^{-4.2x}

y(0)=1, y^{'}(0)=1

y(x)=?

The way I tried to achieve is to solve the corresponding homo equation first:

y^{''}+8.4y^{'}+17.64y=0, which gives y_{c};

y_{c}=c_{1}e^{-4.2x}+c_{2}e^{-4.2x}x

Then try to find y_{p}, generally I would assume a y_{p}=Ae^{-4.2x}, but from the y_{c}got above, clearly y_{p}=Ae^{-4.2x}or y_{p}=Ae^{-4.2x}x is not good. If I add one more 'x' in y_{p}assumption,in which it seems A has to be 0, which is not right either....

Any idea? Or I made some mistake?

Meric.

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# A tricky 2nd Oder ODE Problem,nonhomo delta=0 case

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